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Beauville Surfaces and Groups

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Ingrid Bauer

    1. Lehrstuhl Mathematik VIII, University of Bayreuth, Bayreuth, Germany

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  2. Shelly Garion

    1. Institut für Mathematische Logik und Gru, University of Münster, Münster, Germany

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  3. Alina Vdovina

    1. School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne, United Kingdom

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Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 123)

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Table of contents (11 papers)

  1. Front Matter

    Pages i-ix
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  2. The Fundamental Group and Torsion Group of Beauville Surfaces

    • Ingrid Bauer, Fabrizio Catanese, Davide Frapporti
    Pages 1-14

  3. Regular Algebraic Surfaces, Ramification Structures and Projective Planes

    • N. Barker, N. Boston, N. Peyerimhoff, A. Vdovina
    Pages 15-33

  4. A Survey of Beauville \(p\)-Groups

    • Nigel Boston
    Pages 35-40

  5. Strongly Real Beauville Groups

    • Ben Fairbairn
    Pages 41-61

  6. Beauville Surfaces and Probabilistic Group Theory

    • Shelly Garion
    Pages 63-78

  7. The Classification of Regular Surfaces Isogenous to a Product of Curves with \(\chi ({\mathcal {O}}_S)= 2\)

    • Christian Gleißner
    Pages 79-95

  8. Characteristically Simple Beauville Groups, II: Low Rank and Sporadic Groups

    • Gareth A. Jones
    Pages 97-120

  9. Remarks on Lifting Beauville Structures of Quasisimple Groups

    • Kay Magaard, Christopher Parker
    Pages 121-128

  10. Surfaces Isogenous to a Product of Curves, Braid Groups and Mapping Class Groups

    • Matteo Penegini
    Pages 129-148

  11. On Quasi-Étale Quotients of a Product of Two Curves

    • Roberto Pignatelli
    Pages 149-170

  12. Isotrivially Fibred Surfaces and Their Numerical Invariants

    • Francesco Polizzi
    Pages 171-183
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Keywords

About this book

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces.

Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject.

These proceedings reflect the topics of the lectures presented during the workshop ‘Beauville surfaces and groups 2012’, held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.

Editors and Affiliations

  • Lehrstuhl Mathematik VIII, University of Bayreuth, Bayreuth, Germany

    Ingrid Bauer

  • Institut für Mathematische Logik und Gru, University of Münster, Münster, Germany

    Shelly Garion

  • School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne, United Kingdom

    Alina Vdovina

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