Kollár Shafarevich Maps and Automorphic Forms

Course Book
ISBN: 978-1-4008-6419-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 212 Seiten

Reihe: Princeton Legacy Library

No detailed description available for "Shafarevich Maps and Automorphic Forms".

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