Author | Holzapfel, Rolf-Peter. author |
---|---|
Title | Ball and Surface Arithmetics [electronic resource] / by Rolf-Peter Holzapfel |
Imprint | Wiesbaden : Vieweg+Teubner Verlag, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-322-90169-9 |
Descript | XIV, 414p. online resource |
1 Abelian Points -- 1.1 Cyclic Points -- 1.2 Graphs of Abelian Points -- 1.3 Geometric Interpretation -- 1.4 Derived Representations -- 1.5 The Differential Relation -- 1.6 Stepwise Resolutions of Cyclic Points -- 1.7 Continued Fractions and Selfintersection Numbers -- 1.8 Reciprocity Law for Geometric Sums -- 1.9 Explicit Dedekind Sums -- 1.10 Eisenstein Sums -- 1.11 Hirzebruchโs Sum -- 1.12 Geometric Interpretation -- 1.13 Quotients and Coverings of Modifications -- 1.14 Selfintersections of Quotient Curves -- 1.15 The Bridge Algorithm -- 1.16 First Orbital Properties -- 1.17 Local Orbital Euler Numbers -- 1.18 Absorptive Numbers -- 2 Orbital Curves -- 2.1 Point Arrangements on Curves -- 2.2 Euler Heights of Orbital Curves -- 2.3 The Geometric Local-Global Principle -- 2.4 Signature Heights of Orbital Curves -- 3 Orbital Surfaces -- 3.1 Regular Arrangements on Surfaces -- 3.2 Basic Invariants and Fixed Point Theorem -- 3.3 Euler Heights -- 3.4 Signature Heights -- 3.5 Quasi-homogeneous Points, Quotient Points and Cusp Points -- 3.6 Quasi-smooth Orbital Surfaces -- 3.7 Open Orbital Surfaces -- 3.8 Orbital Decompositions -- 4 Ball Quotient Surfaces -- 4.1 Ball Lattices -- 4.2 Neat Ball Cusp Lattices -- 4.3 Invariants of Neat Ball Quotient Surfaces -- 4.4 ?-Rational Discs -- 4.5 Cusp Singularities, Reflections and Elliptic Points -- 4.6 Orbital Ball Quotient Surfaces and Molecular -- 4.7 Invariants of Disc Quotient Curves -- 4.8 Invariants of Ball Quotient Surfaces -- 4.9 Global Proportionality -- 4.10 Orbital Decompositions and the Finiteness Theorem -- 4.11 Leading Examples -- 4.12 Towards the Count of Ball Metrics on Non-Compact Surfaces -- 5 Picard Modular Surfaces -- 5.1 Classification Diagram -- 5.2 Picard Modular Surface of the Field of Eisenstein Numbers -- 5.3 Picard Modular Surface of the Field of Gauss-Numbers -- 5.4 Kodaira Classification of Picard Modular Surfaces -- 5.5 Special Results and Examples -- 5A Volumes of Fundamental Domains of Picard Modular Groups -- 5A.1 The Order of Finite Unitary Groups -- 5A.2 Index of Congruence Subgroups -- 5A.3 Local Volumina -- 5A.4 The Global Volume -- 6 ?-Orbital Surfaces -- 6.1 Introduction -- 6.2 Arrangements with Rational Coefficients -- 6.3 Finite Morphisms of ?-Orbital Surfaces -- 6.4 Functorial Properties for Rational Invariants -- 6.5 Euler and Signature Heights -- 6.6 Reduction of Galois-Finite Morphisms -- 6.7 Local Base Changes -- 6.8 Global Base Changes -- 6.9 Explicit Hurwitz Formulas for Finite Surface Coverings -- 6.10 Finite Coverings of Ruled Surfaces and the Inequality c12 ? 2c2