Beauville complex algebraic surfaces pdf download

PDF Back to top About this book The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. filexlib. This book is available in ePub and PDF format with a single click unlimited downloads. 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. By generalising Beauville's original example [4, p. 159], they can be constructed from finite groups acting on suitable pairs of algebraic curves, and here we give some new examples of families of groups which can be used for this purpose. A Beauville surface of unmixed type is a compact complex surface S such that
Download Free PDF Recent work on Beauville surfaces, structures and groups Ben Fairbairn Abstract Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. For complex surfaces S an analogous criterion in which Belyi functions are replaced by Lefschetz functions is given in [6]. Among the complex surfaces de ned over a number eld an important class is that of Beauville surfaces de ned as follows De nition [4] A Beauville surface is a compact complex surface Ssatisfying the following properties:
In mathematics, a Beauville surface is one of the surfaces of general type introduced by Arnaud Beauville (1996, exercise X.13 (4)).They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces.. Construction. Let C 1 and C 2 be smooth curves with genera g 1 and g 2.Let G be a finite group acting on C 1 and C 2 such that . G has order (g 1 − 1)(g 2 − 1)
Beauville surfaces and probabilistic group theory Shelly Garion A Beauville surface is a complex algebraic surface that can be presented as a quotient of a product of two curves by a suitable action of a finite group.
Beauville surfaces and finite groups @article{Fuertes2009BeauvilleSA, title={Beauville surfaces and finite groups}, author={Yolanda Fuertes and Gareth Aneurin Jones}, journal={arXiv: Group Theory}, year={2009} } Y. Fuertes, G. Jones; Published 28 October 2009; Mathematics; arXiv: Group Theory
Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. In this survey we discuss the groups that may be used in this way.
The classification of algebraic surfaces is an intricate and fascinating branch of mathematics, developed over more than a century and still an active area of research today. In this book, Professor Beauville gives a lucid and concise account of the subject, expressed simply in the language of modern topology and sheaf theory, and accessible to
Journal of Algebra340 (2011) 13-27 Contents lists available at ScienceDirect JournalofAlgebra elsevier.com/locate/jalgebra Beauvillesurfacesandfinitegroups
Algebraic geometers such as Bauer, Catanese and Grunewald have recently initiated the study of Beauville surfaces. These are 2-dimensional complex algebraic varieties which are rigid, in the sense of admitting no de