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

Paula Tretkoff

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Geometrie

Beschreibung

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.

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Schlagwörter

Homomorphism, Complex plane, Covering space, Surface of general type, Theorem, Differential geometry, Fuchsian group, Normal subgroup, Division by zero, Compact Riemann surface, Lie group, Projective space, Natural number, Coefficient, Curvature, Permutation, Line bundle, Ricci curvature, Complex analysis, Cohomology, Partial differential equation, Subgroup, Riemann surface, Complex dimension, Divisor, Differential equation, Volume form, Conjugacy class, Euler number, Dimension, Princeton University, Fundamental group, Conjecture, Elliptic curve, Hypergeometric function, Adjunction formula, Riemann sphere, Connected space, Icosahedron, Monodromy, Meromorphic function, Orbifold, Quadratic form, Triangle group, Projective line, Algebraic surface, Projective plane, Triple point, Finite set, Homology (mathematics), Algebraic group, Differential form, Homotopy, Complex number, Complex manifold, Embedding, Two-dimensional space, Vector space, Equivalence class, Tangent space, Algebraic variety, Automorphism, Betti number, Unit disk, Complex projective plane, Compactification (mathematics), Holomorphic function, Special case, Submanifold, Gaussian curvature