Shafarevich Maps and Automorphic Forms

János Kollár

Published by Princeton University Press 1995

Shafarevich Maps and Automorphic Forms

János Kollár

In the series Princeton Legacy Library

Volume 7 in the series Porter Lectures

https://doi.org/10.1515/9781400864195

Overview
Contents

About this book

The aim of this book is to study various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the theory of harmonic maps, and topology. Making systematic use of Shafarevich maps, a concept previously introduced by the author, this work isolates those varieties where the fundamental group influences global properties of the canonical class.

The book is primarily geared toward researchers and graduate students in algebraic geometry who are interested in the structure and classification theory of algebraic varieties. There are, however, presentations of many other applications involving other topics as well--such as Abelian varieties, theta functions, and automorphic forms on bounded domains. The methods are drawn from diverse sources, including Atiyah's L2 -index theorem, Gromov's theory of Poincaré series, and recent generalizations of Kodaira's vanishing theorem.

Originally published in 1995.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Reviews

I believe Kollár has written a powerful book, and not coincidentally, a fairly demanding one. However, the explanations are clear, and I think that more than half of it would be accessible to anyone who has mastered the basics of complex algebraic geometry.... There are a number of sections ... which could be read independently of the rest of the book and would be of interest to almost any algebraic geometer. But to read only those sections would be a shame, because one would be missing a great deal of wonderful mathematics.

Topics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	v
PREFACE Requires Authentication Unlicensed Licensed Download PDF	vii
ACKNOWLEDGMENTS Requires Authentication Unlicensed Licensed Download PDF	ix
INTRODUCTION Requires Authentication Unlicensed Licensed Download PDF	1
Part I. Shafarevich Maps Requires Authentication Unlicensed Licensed Download PDF	17
Part II. Automorphic Forms: Classical Theory Requires Authentication Unlicensed Licensed Download PDF	57
PART III. VANISHING THEOREMS Requires Authentication Unlicensed Licensed Download PDF	103
Part IV. Automorphic Forms Revisited Requires Authentication Unlicensed Licensed Download PDF	139
Part V. Other Applications and Speculations Requires Authentication Unlicensed Licensed Download PDF	173
REFERENCES Requires Authentication Unlicensed Licensed Download PDF	191
INDEX Requires Authentication Unlicensed Licensed Download PDF	201

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