Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published by Princeton University Press 2016

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

In collaboration with: Hans-Christoph Im Hof

Volume 51 in the series Mathematical Notes

https://doi.org/10.1515/9781400881253

Overview
Contents

About this book

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 quotients 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.

Author information

Paula Tretkoff is professor of mathematics at Texas A&M University and director of research in the National Center for Scientific Research (CNRS) at the Université de Lille 1, France.

Reviews

A very welcome addition to the literature and is recommended for anyone interested in the theory under discussion.---Daniel Greb, MathSciNet

Topics

Frontmatter Accessible Download PDF	i
Contents Accessible Download PDF	vii
Preface Requires Authentication Accessible Download PDF	ix
Introduction Requires Authentication Accessible Download PDF	1
Chapter One. Topological Invariants and Differential Geometry Requires Authentication Accessible Download PDF	6
Chapter Two. Riemann Surfaces, Coverings, and Hypergeometric Functions Requires Authentication Accessible Download PDF	23
Chapter Three. Complex Surfaces and Coverings Requires Authentication Accessible Download PDF	47
Chapter Four. Algebraic Surfaces and the Miyaoka-Yau Inequality Requires Authentication Accessible Download PDF	65
Chapter Five. Line Arrangements in P2(C) and Their Finite Covers Requires Authentication Accessible Download PDF	85
Chapter Six. Existence of Ball Quotients Covering Line Arrangements Requires Authentication Accessible Download PDF	126
Chapter Seven. Appell Hypergeometric Functions Requires Authentication Accessible Download PDF	167
Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof Requires Authentication Accessible Download PDF	189
Appendix B. Kummer Coverings Requires Authentication Accessible Download PDF	197
Bibliography Requires Authentication Accessible Download PDF	205
Index Requires Authentication Accessible Download PDF	213