Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51) / Paula Tretkoff.

Format:

Book

Author/Creator:

Tretkoff, Paula, author.

Contributor:

Im Hof, Hans-Christoph.

Series:

Mathematical notes (Princeton University Press) ; 51.

Mathematical Notes ; 51

Language:

English

Subjects (All):

Curves, Elliptic.

Geometry, Algebraic.

Projective planes.

Unit ball.

Riemann surfaces.

Physical Description:

1 online resource (229 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free "ients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function.The material in this book began as a set of lecture notes, taken by Tretkoff, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded by Hirzebruch and Tretkoff over a number of years. In this book, Tretkoff has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers.Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.

Contents:

Frontmatter

Contents

Preface

Introduction

Chapter One. Topological Invariants and Differential Geometry

Chapter Two. Riemann Surfaces, Coverings, and Hypergeometric Functions

Chapter Three. Complex Surfaces and Coverings

Chapter Four. Algebraic Surfaces and the Miyaoka-Yau Inequality

Chapter Five. Line Arrangements in P2(C) and Their Finite Covers

Chapter Six. Existence of Ball Quotients Covering Line Arrangements

Chapter Seven. Appell Hypergeometric Functions

Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof

Appendix B. Kummer Coverings

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

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

ISBN:

9781400881253

1400881250

OCLC:

934433896