ISBN-10:
0821821563
ISBN-13:
9780821821565
Pub. Date:
11/14/2001
Publisher:
American Mathematical Society
Advances in Moduli Theory

Advances in Moduli Theory

by Kenji Ueno, Y. Shimizu

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Product Details

ISBN-13: 9780821821565
Publisher: American Mathematical Society
Publication date: 11/14/2001
Series: Translations of Mathematical Monographs , #206
Edition description: New Edition
Pages: 300
Product dimensions: 5.66(w) x 8.30(h) x 1.57(d)

Table of Contents

Prefaceix
Preface to the English Translationxiii
Summary and Overview of the Theoryxv
Chapter 1.Kodaira-Spencer Mapping1
1.1.Deformation of complex structures2
1.2.Infinitesimal deformation of a principal bundle31
Summary34
Chapter 2.Torelli's Theorem35
2.1.Complex torus and abelian variety36
2.2.Jacobian varieties56
2.3.Torelli's theorem78
2.4.Period mappings91
Summary99
Chapter 3.Period Mappings and Hodge Theory101
3.1.Hodge Structure and period domain102
3.2.Period mappings and Torelli problems130
3.3.Period mappings and mixed Hodge structure149
Summary174
Chapter 4.Conformal Field Theory177
4.1.Stable pointed curves and their moduli182
4.2.Conformal blocks193
4.3.Sheaf of conformal blocks and connection232
4.4.KZ equations256
4.5.Verlinde formula260
Summary278
Prospects and Remaining Problems279
Solutions to Problems285
Bibliography291
Index297

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