Complex Ball Quotients and Line Arrangements in the Projective Plane MN 51 Mathematical Notes 51 1st Edition by Paula Tretkoff 9781400881253 1400881250

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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