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Geometry of Moduli

Author: Jan Arthur Christophersen; Kristian Ranestad
Publisher: Cham : Springer Nature : Springer, 2018.
Series: Abel symposia, v. 14.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Geometry of Moduli.
Cham : Springer Nature : Springer, 2018
(OCoLC)1039613742
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jan Arthur Christophersen; Kristian Ranestad
ISBN: 9783319948812 3319948814
OCLC Number: 1076543339
Description: 1 online resource : illustrations
Contents: Intro; Foreword; Preface; Contents; Stratifying Quotient Stacks and Moduli Stacks; 1 Introduction; 2 Classical and Non-reductive GIT; 2.1 Classical GIT for Reductive Groups; 2.1.1 The HKKN Stratification; 2.1.2 Partial Desingularisations of Reductive GIT Quotients; 2.2 GIT for Non-reductive Groups; 2.3 GIT for Linear Algebraic Groups with Internally Graded Unipotent Radicals; 3 Stratifying Quotient Stacks; 4 Stacks Filtered by Quotient Stacks; 5 Applications; 5.1 Moduli of Hypersurfaces in a Complete Toric Variety; 5.2 Moduli of Sheaves Over a Projective Scheme; 5.3 Moduli of Unstable Curves 3.2 Tangent Space3.3 Elementary Modifications; 3.4 Comparing Components; 3.4.1 Separating Two Loci; 3.4.2 Separating Multiple Loci; 4 Brill-Noether Theorems; 4.1 Rank 1 Sheaves; 4.2 The Projective Plane; 4.3 Hirzebruch Surfaces; 4.4 Del Pezzo Surfaces and More General Rational Surfaces; 4.5 Other Surfaces; References; Geometric Invariant Theory of Syzygies, with Applications to Moduli Spaces; 1 Introduction; 1.1 Notation and Conventions; 2 Syzygy Points; 3 Families of Polarized Varieties; 3.1 Summation Formulae; 4 K3 Surfaces; 4.1 Effective Divisors on the Moduli Space of K3 Surfaces 5 Canonical Curves5.1 Hassett-Keel Program for Mg and Syzygies; 6 GIT for Syzygies of Canonical Genus Six Curves; 6.1 Clifford Index 1; 6.2 Clifford Index 2; 6.2.1 Bielliptic Curves and Elliptic Ribbons; 6.2.2 Singular Degree 5 del Pezzo; 6.3 The Hassett-Keel Program for M6; 6.3.1 Future Directions; References; The Topology of Ag and Its Compactifications; 1 Introduction; 2 The Complex Analytic Approach; 3 The Tautological Ring of Ag; 4 Compactifications and the Proportionality Principle; 5 L2 Cohomology and Zucker's Conjecture; 6 Computations in Small Genus; 7 Stabilization Results
Series Title: Abel symposia, v. 14.
Responsibility: Jan Authur Christophersen, Kristian Ranestad, editors.

Abstract:

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinoya Rorbuer, Svolvaer in Lofoten, in August 2017, present both survey and research articles on the recent surge of  Read more...

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