Geer, Gerard van der
Overview
Works:  44 works in 211 publications in 1 language and 3,309 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Other 
Classifications:  QA268, 003.54 
Publication Timeline
.
Most widely held works by
Gerard van der Geer
Hilbert modular surfaces by
Gerard van der Geer(
Book
)
16 editions published between 1987 and 1988 in English and Undetermined and held by 385 WorldCat member libraries worldwide
Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples  in fact a whole chapter  completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field
16 editions published between 1987 and 1988 in English and Undetermined and held by 385 WorldCat member libraries worldwide
Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples  in fact a whole chapter  completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field
Introduction to coding theory by
Jacobus Hendricus van Lint(
Book
)
13 editions published in 1988 in English and held by 354 WorldCat member libraries worldwide
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 1621, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the GilbertVarshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI  CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
13 editions published in 1988 in English and held by 354 WorldCat member libraries worldwide
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 1621, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the GilbertVarshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI  CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Arithmetic algebraic geometry by
J Oesterlé(
Book
)
15 editions published in 1991 in English and Undetermined and held by 299 WorldCat member libraries worldwide
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin's work, Ktheory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the BirchSwinnertonDyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this stateoftheart selection
15 editions published in 1991 in English and Undetermined and held by 299 WorldCat member libraries worldwide
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin's work, Ktheory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the BirchSwinnertonDyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this stateoftheart selection
The moduli space of curves by
R Dijkgraaf(
Book
)
10 editions published in 1995 in English and held by 288 WorldCat member libraries worldwide
The moduli space Mg of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteens conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory
10 editions published in 1995 in English and held by 288 WorldCat member libraries worldwide
The moduli space Mg of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteens conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory
Number fields and function fields : two parallel worlds by
Gerard van der Geer(
Book
)
24 editions published between 2005 and 2007 in English and held by 234 WorldCat member libraries worldwide
Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and tmotives
24 editions published between 2005 and 2007 in English and held by 234 WorldCat member libraries worldwide
Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and tmotives
Moduli of Abelian varieties by
C Faber(
Book
)
14 editions published in 2001 in English and held by 219 WorldCat member libraries worldwide
Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics
14 editions published in 2001 in English and held by 219 WorldCat member libraries worldwide
Abelian varieties and their moduli are a central topic of increasing importance in today`s mathematics. Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field. The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics
Lectures on Hilbert modular surfaces by
Friedrich Hirzebruch(
Book
)
10 editions published in 1981 in English and Undetermined and held by 179 WorldCat member libraries worldwide
10 editions published in 1981 in English and Undetermined and held by 179 WorldCat member libraries worldwide
Modular forms on schiermonnikoog by
B Edixhoven(
Book
)
11 editions published in 2008 in English and held by 128 WorldCat member libraries worldwide
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspiration for Langlands' conjectures and play an important role in the description of the cohomology of varieties defined over number fields. This collection of uptodate articles originated from the conference 'Modular Forms' held on the Island of Schiermonnikoog in the Netherlands. A broad range of topics is covered including Hilbert and Siegel modular forms, Weil representations, Tannakian categories and Torelli's theorem. This book is a good source for all researchers and graduate students working on modular forms or related areas of number theory and algebraic geometry
11 editions published in 2008 in English and held by 128 WorldCat member libraries worldwide
Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today. Modular forms formed the inspiration for Langlands' conjectures and play an important role in the description of the cohomology of varieties defined over number fields. This collection of uptodate articles originated from the conference 'Modular Forms' held on the Island of Schiermonnikoog in the Netherlands. A broad range of topics is covered including Hilbert and Siegel modular forms, Weil representations, Tannakian categories and Torelli's theorem. This book is a good source for all researchers and graduate students working on modular forms or related areas of number theory and algebraic geometry
Classification of algebraic varieties by
E Looijenga(
Book
)
10 editions published in 2011 in English and held by 100 WorldCat member libraries worldwide
Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers
10 editions published in 2011 in English and held by 100 WorldCat member libraries worldwide
Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers
K3 surfaces and their moduli(
Book
)
16 editions published in 2016 in English and held by 58 WorldCat member libraries worldwide
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like zThe Moduli Space of Curvesy and zModuli of Abelian Varieties,y which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. NieperWisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin
16 editions published in 2016 in English and held by 58 WorldCat member libraries worldwide
This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like zThe Moduli Space of Curvesy and zModuli of Abelian Varieties,y which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. NieperWisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin
On Hilbert modular surfaces of principal congruence subgroups by
Gerard van der Geer(
Book
)
8 editions published between 1950 and 1977 in English and Undetermined and held by 20 WorldCat member libraries worldwide
8 editions published between 1950 and 1977 in English and Undetermined and held by 20 WorldCat member libraries worldwide
The moduli space of abelian varieties and the singularities of the theta divisor by
C Ciliberto(
Book
)
3 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1999 in English and held by 4 WorldCat member libraries worldwide
The 123 of modular forms : lectures at a summer school in Nordfjordeid, Norway by
Jan H Bruinier(
Book
)
5 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
This book grew out of three series of lectures given at the summer school on 'Modular Forms and their Applications' held in Nordfjordeid in June 2004
5 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
This book grew out of three series of lectures given at the summer school on 'Modular Forms and their Applications' held in Nordfjordeid in June 2004
Curves over finite fields of characteristic two with many rational points by
Gerard van der Geer(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we construct curves over finite fields in characteristic 2 with many rational points. The methods of construction are inspired by considerations from coding theory."
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we construct curves over finite fields in characteristic 2 with many rational points. The methods of construction are inspired by considerations from coding theory."
On generalized Hamming weights of BCHcodes by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Subvarieties of the Moduli Space of Curves parametrizing Jacobians with nontrivial endomorphisms by
C Ciliberto(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
Supersingular curves of genus 2 over finite fields of characteristic 2 by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
The second generalized Hamming weight of the dual codes of doubleerror correcting binary BCHcodes by
Gerard van der Geer(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerrorcorrecting BCHcodes."
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "In this note we determine the second generalized Hamming weight of the dual codes of binary doubleerrorcorrecting BCHcodes."
Kloosterman sums and the ptorsion of certain Jacobians by
Gerard van der Geer(
Book
)
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 3 WorldCat member libraries worldwide
Fibre products of artinschreier curves and generalized hamming weight of codes by
Gerard van der Geer(
Book
)
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 3 WorldCat member libraries worldwide
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Related Identities
 Faber, C. (Carel) 1962 Other Author Editor
 Moonen, Ben Editor
 Schoof, René Editor
 Oort, Frans 1935 Other Editor
 Lint, Jacobus Hendricus van 1932 Author
 Steenbrink, J. H. M. Editor
 Dijkgraaf, R. Other Editor
 Farkas, Gavril Editor
 Edixhoven, B. (Bas) 1962 Author Editor
 Hirzebruch, Friedrich Author
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Associated Subjects
Abelian varieties Algebra Algebraic fields Algebraic topology Algebraic varietiesClassification theory Arithmetical algebraic geometry Coding theory Combinatorial analysis Curves, Algebraic Endomorphisms (Group theory) Errorcorrecting codes (Information theory) Finite fields (Algebra) Forms, Modular Geometry, Algebraic Hilbert modular surfaces Isomorphisms (Mathematics) Jacobi sums Kloosterman sums Ktheory Mathematical physics Mathematics Moduli theory Number theory Physics Surfaces Surfaces, Algebraic Topology
Alternative Names
De Geer, Gerard
Der Geer Gerard van
Geer, G. van der
Geer, G. van der 1950
Geer, G. van der (Gerard van der)
Geer, Gerardus Bartholomeus Maria van der
Geer, Gerardus Bartholomeus Maria van der 1950
Gerard van der Geer niederländischer Mathematikhistoriker
Van der Geer Gerard
Van der Geer, Gerard 1950
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