Book

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

Paula Tretkoff

Published by Princeton University Press

Published in print February 2016 | ISBN: 9780691144771
Published online October 2017 | e-ISBN: 9781400881253
Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

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This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that are free quotients of the complex 2-ball. The book also includes a background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The book began as a set of lecture notes, taken by the author, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded over a number of years. In this book, the author 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.

Keywords: complex surface; line arrangement; Gauss hypergeometric function; Appell hypergeometric function; Friedrich Hirzebruch; finite covering; geometry; projective plane; complex 2-ball

Book.  232 pages.  Illustrated.

Subjects: Geometry

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Table of Contents

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

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Topological Invariants and Differential Geometry in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

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Riemann Surfaces, Coverings, and Hypergeometric Functions in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

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

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Algebraic Surfaces and the Miyaoka-Yau Inequality in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

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Line Arrangements in P2(C) and Their Finite Covers in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

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

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

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