Beauville Surfaces and Groups

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.

Inhalt

Introduction.- THE FUNDAMENTAL GROUP AND TORSION GROUP OF BEAUVILLE SURFACES.- REGULAR ALGEBRAIC SURFACES, RAMIFICATION STRUCTURES AND PROJECTIVE PLANES.- A SURVEY OF BEAUVILLE p-GROUPS.- STRONGLY REAL BEAUVILLE GROUPS.- BEAUVILLE SURFACES AND PROBABILISTIC GROUP THEORY.- The Classification of Regular Surfaces Isogenous to a Product of Curves with $\chi(\mathcal O_S) = 2$.- : Characteristically simple Beauville groups, II: low rank and sporadic groups.- REMARKS ON LIFTING BEAUVILLE STRUCTURES OF QUASISIMPLE GROUPS.- SURFACES ISOGENOUS TO A PRODUCT OF CURVES, BRAID GROUPS AND MAPPING CLASS GROUPS.- ON QUASI-{'E}TALE QUOTIENTS OF A PRODUCT OF TWO CURVES.- Isotrivially fibred surfaces and their numerical invariants.