Kollár Shafarevich Maps and Automorphic Forms

Course Book
ISBN: 978-1-4008-6419-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 212 Seiten

Reihe: Princeton Legacy Library

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.

Autoren/Hrsg.

Kollár, János

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Preface

Acknowledgments

Introduction 3

Ch. 1 Lefschetz-Type Theorems for [pi][subscript 1] 19

Ch. 2 Families of Algebraic Cycles 27

Ch. 3 Shafarevich Maps and Variants 36

Ch. 4 The Fundamental Group and the Classification of Algebraic Varieties 49

Ch. 5 The Method of Poincare 59

Ch. 6 The Method of Atiyah 71

Ch. 7 Subjectivity of the Poincare Map 81

Ch. 8 Ball Quotients 92

Ch. 9 The Kodaira Vanishing Theorem 105

Ch. 10 Generalizations of the Kodaira Vanishing Theorem 115

Ch. 11 Vanishing of L[superscript 2]-Cohomologies 127

Ch. 12 Rational Singularities and Hodge Theory 133

Ch. 13 The Method of Gromov 141

Ch. 14 Nonvanishing Theorems 151

Ch. 15 Plurigenera in Etale Covers 161

Ch. 16 Existence of Automorphic Forms 167

Ch. 17 Applications to Abelian Varieties 175

Ch. 18 Open Problems and Further Remarks 183

References 191

Index 201