Complex Ball Quotients and Line Arrangements in the Projective Plane MN 51 Mathematical Notes 51 1st Edition Paula Tretkoff – Ebook PDF Instant Download/Delivery, ISBN: 9781400881253, 1400881250
Product details:
- ISBN 10:1400881250
- ISBN 13:9781400881253
- Author: Paula Tretkoff
Complex Ball Quotients and Line Arrangements in the Projective Plane
Table contents:
1: Topological Invariants and Differential Geometry
1.1: Topological Invariants
1.2: Fundamental Groups and Covering Spaces
1.3: Complex Manifolds and Metrics
1.4: Divisors, Line Bundles, the First Chern Class
2: Riemann Surfaces, Coverings, and Hypergeometric Functions
2.1: Genus and Euler Number
2.2: Möbius Transformations
2.3: Metric and Curvature
2.4: Behavior of the Euler Number under Finite Covering
2.5: Finite Subgroups of PSL(2, ℂ)
2.6: Gauss Hypergeometric Functions
2.7: Triangle Groups
2.8: The Hypergeometric Monodromy Group
3: Complex Surfaces and Coverings
3.1: Coverings Branched over Subvarieties with Transverse Intersections
3.2: Divisor Class Group and Canonical Class
3.3: Proportionality
3.4: Signature
3.5: Blowing Up Points
4: Algebraic Surfaces and the Miyaoka-Yau Inequality
4.1: Rough Classification of Algebraic Surfaces
4.2: The Miyaoka-Yau Inequality, I
4.3: The Miyaoka-Yau Inequality, II
5: Line Arrangements in ℙ₂(ℂ) and Their Finite Covers
5.1: Blowing Up Line Arrangements
5.2: Höfer’s Formula
5.3: Arrangements Annihilating R and Having Equal Ramification along All Lines
5.4: Blow-Up of a Singular Intersection Point
5.5: Possibilities for the Assigned Weights
5.6: Blowing Down Rational Curves and Removing Elliptic Curves
5.7: Tables of the Weights Giving Prop = 0
6: Existence of Ball Quotients Covering Line Arrangements
6.1: Existence of Finite Covers by Ball Quotients of Weighted Configurations: The General Case
6.2: Remarks on Orbifolds and b-Spaces
6.3: Kᵪ,, + D″ for Weighted Line Arrangements
6.4: Existence Question
6.5: Ampleness of Kᵪ,, + D″
6.6 Log-Terminal Singularities and LCS
6.7: Existence Theorem for Line Arrangements
6.8: Isotropy Subgroups of the Covering Group
7: Appell Hypergeometric Functions
7.1: The Action of S₅ on the Blown-Up Projective Plane
7.2: Appell Hypergeometric Functions
7.3: Arithmetic Monodromy Groups
7.4: Some Remarks about the Signature
A: Torsion-Free Subgroups of Finite Index
A.1: Fuchsian Groups
A.2: Fenchel’s Conjecture
A.3: Reduction to Triangle Groups
A.4: Triangle Groups
B: Kummer Coverings
Bibliography
Index
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