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Advances in moduli theory

Author: Kenji Ueno; Y Shimizu
Publisher: Providence, R.I. : American Mathematical Society, ©2002.
Series: Translations of mathematical monographs, v. 206.; Iwanami series in modern mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This book aims to study several aspects of moduli theory from a complex analytic point of view. Chapter 1 gives a brief introduction to the Kodaira-Spencer deformation theory of compact complex manifolds. In Chapter 2 we discuss the analytic theory of abelian varieties, and show how to construct the moduli theory of polarized abelian varieties. Also the moduli of closed Riemann surfaces and Torelli's theorem will  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Kenji Ueno; Y Shimizu
ISBN: 0821821563 9780821821565
OCLC Number: 47716471
Language Note: Translated from the Japanese.
Notes: Authors' names on t.p. of translation reversed from original.
Description: xix, 300 pages : illustrations ; 22 cm.
Contents: Kodaira-Spencer Mapping --
Deformation of complex structures --
Infinitesimal deformation of a principal bundle --
Torelli's Theorem --
Complex torus and abelian variety --
Jacobian varieties --
Torelli's theorem --
Period mappings --
Period Mappings and Hodge Theory --
Hodge Structure and period domain --
Period mappings and Torelli problems --
Period mappings and mixed Hodge structure --
Conformal Field Theory --
Stable pointed curves and their moduli --
Conformal blocks --
Sheaf of conformal blocks and connection --
KZ equations --
Verlinde formula --
Prospects and Remaining Problems.
Series Title: Translations of mathematical monographs, v. 206.; Iwanami series in modern mathematics.
Other Titles: Mojurai riron 3.
Responsibility: Yuji Shimizu, Kenji Ueno ; translated by Yuji Shimizu, Kenji Ueno.

Abstract:

Presents the Kodaira-Spencer theory in its original naive form. This book introduces readers to moduli theory from the viewpoint of complex analytic geometry. It outlines the theory of period mapping  Read more...

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   schema:reviewBody ""This book aims to study several aspects of moduli theory from a complex analytic point of view. Chapter 1 gives a brief introduction to the Kodaira-Spencer deformation theory of compact complex manifolds. In Chapter 2 we discuss the analytic theory of abelian varieties, and show how to construct the moduli theory of polarized abelian varieties. Also the moduli of closed Riemann surfaces and Torelli's theorem will be discussed. Chapter 3 gives the basics of Hodge theory. In the final chapter, as an application of the moduli theory of curves we shall discuss non-abelian conformal field theory as formulated by Tsuchiya, Ueno, and Yamada. Its relation to the moduli of vector bundles on a closed Riemann surface will also be discussed." "The book is aimed at graduate and upper-level undergraduate students who want to learn modern moduli theory."--BOOK JACKET." ;
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