Advances in Moduli Theory
( Translations of Mathematical Monographs )
Publication series ： Translations of Mathematical Monographs
Author： Yuji Shimizu;Kenji Ueno
Publisher： American Mathematical Society
Publication year： 2018
E-ISBN: 9781470446314
P-ISBN(Paperback): 9780821821565
Subject： O153.3 Ring theory
Keyword： 数学
Language： ENG
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
Advances in Moduli Theory
Description
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.
Chapter