Description
Book SynopsisThis 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
Trade Review"A very welcome addition to the literature and is recommended for anyone interested in the theory under discussion."--Daniel Greb, MathSciNet
Table of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. ix*Introduction, pg. 1*Chapter One. Topological Invariants and Differential Geometry, pg. 6*Chapter Two. Riemann Surfaces, Coverings, and Hypergeometric Functions, pg. 23*Chapter Three. Complex Surfaces and Coverings, pg. 47*Chapter Four. Algebraic Surfaces and the Miyaoka-Yau Inequality, pg. 65*Chapter Five. Line Arrangements in P2(C) and Their Finite Covers, pg. 85*Chapter Six. Existence of Ball Quotients Covering Line Arrangements, pg. 126*Chapter Seven. Appell Hypergeometric Functions, pg. 167*Appendix A. Torsion-Free Subgroups of Finite Index by Hans-Christoph Im Hof, pg. 189*Appendix B. Kummer Coverings, pg. 197*Bibliography, pg. 205*Index, pg. 213
