Shafarevich Maps and Automorphic Forms (ebook)

Argumento de Shafarevich Maps and Automorphic Forms (ebook)

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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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 1905.0Preface 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