Beauville Surfaces and Groups

Name: Beauville Surfaces and Groups
Brand: Springer
Price: 96.29 EUR
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Ingrid Bauer Shelly Garion Alina Vdovina(Herausgeber*in)

Springer (Verlag)

1. Auflage

Erschienen am 14. April 2015

IX, 183 Seiten

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978-3-319-13862-6 (ISBN)

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Inhalt

Intro
Contents
Introduction
The Fundamental Group and Torsion Group of Beauville Surfaces
1 Introduction
2 Product-Quotient Surfaces
3 The Fundamental Group
4 Some Applications
References
Regular Algebraic Surfaces, Ramification Structures and Projective Planes
1 Introduction
2 Ramification Structures and Associated Surfaces
2.1 Group Theoretical Structures
2.2 From Ramification Structures to Algebraic Surfaces
3 Groups with Special Presentations
3.1 Ramification Structures for the Group in [15, Example 6.3]
3.2 Ramification Structures for the Groups in [11, Example 3.3]
3.3 Ramification Structures for the Group in [15, Example 6.4]
3.4 Ramification Structures for the Groups of Theorem 3.1 with qge4
3.5 Ramification Structures for the Group in [18, Example 2]
References
A Survey of Beauville p-Groups
1 Introduction
2 Definitions
2.1 Beauville Structures
2.2 p-Groups
3 Beauville Groups in O'Brien Trees
3.1 An Example
3.2 Infinite Paths Through the O'Brien Trees
4 Beauville Groups of Small Order
References
Strongly Real Beauville Groups
1 Introduction
2 The Finite Simple Groups
3 Characteristically Simple Groups
4 The Symmetric and Alternating Groups
5 Almost Simple Groups
6 Nilpotent Groups
References
Beauville Surfaces and Probabilistic Group Theory
1 Beauville Surfaces and Beauville Structures
2 Beauville Surfaces and Finite Simple Groups
3 Hyperbolic Triangle Groups and Their Finite Quotients
4 Beauville Structures for the Group `39`42`"613A``45`47`"603APSL2(q)
4.1 Sketch of the Proof of Theorem 10
4.2 Proof of Theorem 7
5 Beauville Structures for Finite Simple Groups
5.1 Choosing Disjoint Conjugacy Classes
5.2 Frobenius Formula and Witten's Zeta Function
5.3 Character Estimates in Finite Simple Groups
5.4 Finding Generating Pairs
References
The Classification of Regular Surfaces Isogenous to a Product of Curves with ?(mathcalOS)= 2
1 Introduction
2 Surfaces Isogenous to a Product
3 Group Theory, Riemann Surfaces and Combinatorics
4 Moduli Spaces
5 The Algorithm and the Classification Result
5.1 Exceptional Cases for Mainloop1:
5.2 Exceptional Cases for Mainloop2:
References
Characteristically Simple Beauville Groups, II: Low Rank and Sporadic Groups
1 Introduction
2 Background and Method of Proof
3 Generating Cartesian Powers
4 Beauville Structures in Cartesian Powers
5 The Groups L2(q)
6 Counting Triples
7 The Suzuki Groups
8 The Small Ree Groups
9 The Sporadic Simple Groups
9.1 The Mathieu Groups
9.2 Other Small Sporadic Simple Groups
9.3 The Larger Sporadic Simple Groups
10 The Groups L3(q) and U3(q)
10.1 L3(q)
10.2 U3(q)
References
Remarks on Lifting Beauville Structures of Quasisimple Groups
1 Introduction
2 Frattini Covers of Beauville Groups
3 Semidirect Products with Beauville Structures
4 Questions
References
Surfaces Isogenous to a Product of Curves, Braid Groups and Mapping Class Groups
1 Introduction
2 Braid Group and Mapping Class Group
3 Surfaces Isogenous to a Product of Curves
4 Connected Components of the Moduli Space of Surfaces of General Type
References
On Quasi-Étale Quotients of a Product of Two Curves
1 Introduction
2 Quasi-Étale Surfaces
3 Constructing Curves with a Finite Group Action
4 Constructing Quasi-Étale Quotients
4.1 Singularities
4.2 Invariants
5 The Minimality Problem
6 Surfaces of General Type with ?(mathcalOS)=1
References
Isotrivially Fibred Surfaces and Their Numerical Invariants
1 Introduction
2 The Main Result
3 Examples
References

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