Shafarevich Maps and Automorphic Forms / János Kollár.

Format:

Book

Author/Creator:

Kollár, János, author.

Series:

Porter Lectures ; 13

Language:

English

Subjects (All):

Automorphic forms.

Shafarevich maps.

Complex manifolds.

Physical Description:

1 online resource (212 pages) : illustrations.

Edition:

Course Book

Place of Publication:

Princeton, NJ : Princeton University Press, [2014]

Language Note:

English

Summary:

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.

Contents:

Frontmatter

CONTENTS

PREFACE

ACKNOWLEDGMENTS

INTRODUCTION

Part I. Shafarevich Maps

Part II. Automorphic Forms: Classical Theory

PART III. VANISHING THEOREMS

Part IV. Automorphic Forms Revisited

Part V. Other Applications and Speculations

REFERENCES

INDEX

Notes:

"M.B. Porter lectures."

Includes bibliographical references (pages [191]-199) and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9780691636429

0691636427

9780691607900

0691607907

9781400864195

1400864194

OCLC:

973401156