Beauville surfaces without real structures

2006 ◽  
pp. 1-42 ◽  
Author(s):  
Ingrid Bauer ◽  
Fabrizio Catanese ◽  
Fritz Grunewald
Keyword(s):  
Beauville Surfaces

scholarly journals New Beauville surfaces and finite simple groups

2013 ◽  
Vol 142 (3-4) ◽  
pp. 391-408 ◽  
Author(s):  
Shelly Garion ◽  
Matteo Penegini
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Beauville Surfaces

Generation of finite quasisimple groups with an application to groups acting on Beauville surfaces

2013 ◽  
Vol 107 (4) ◽  
pp. 744-798 ◽  
Author(s):  
Ben Fairbairn ◽  
Kay Magaard ◽  
Christopher Parker
Keyword(s):  
Beauville Surfaces

scholarly journals Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces

2020 ◽  
Vol 14 (2) ◽  
pp. 689-704
Author(s):  
Şükran Gül ◽  
Jone Uria-Albizuri
Keyword(s):  
Beauville Surfaces

scholarly journals Automorphism groups of Beauville surfaces

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Gareth A. Jones
Keyword(s):  
Finite Group ◽  
Algebraic Surface ◽  
Automorphism Groups ◽  
Beauville Surfaces ◽  
A Finite Group ◽  
Beauville Surface

Abstract.A Beauville surface of unmixed type is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group

scholarly journals On Beauville surfaces

2011 ◽  
pp. 107-119 ◽  
Author(s):  
Yolanda Fuertes ◽  
Gabino González-Díez ◽  
Andrei Jaikin-Zapirain
Keyword(s):  
Beauville Surfaces

The absolute Galois group acts faithfully on regular dessins and on Beauville surfaces

2015 ◽  
Vol 111 (4) ◽  
pp. 775-796 ◽  
Author(s):  
Gabino González-Diez ◽  
Andrei Jaikin-Zapirain
Keyword(s):  
Galois Group ◽  
Absolute Galois Group ◽  
Beauville Surfaces ◽  
The Absolute

Beauville Surfaces

2016 ◽  
pp. 225-249
Author(s):  
Gareth A. Jones ◽  
Jürgen Wolfart
Keyword(s):  
Beauville Surfaces

scholarly journals Beauville Surfaces with Abelian Beauville Group

2014 ◽  
Vol 114 (2) ◽  
pp. 191 ◽  
Author(s):  
G. González-Diez ◽  
G. A. Jones ◽  
D. Torres-Teigell
Keyword(s):  
General Type ◽  
Automorphism Groups ◽  
Free Action ◽  
Rigid Surface ◽  
Isomorphism Classes ◽  
Surface Of General Type ◽  
Beauville Surfaces ◽  
A Finite Group ◽  
Beauville Group ◽  
Beauville Surface

A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves $C_{1}$, $C_{2}$ of genera $g_{1},g_{2}\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\cong \mathsf{Z}_{n}^{2}$ with $\gcd(n,6)=1$ by a result of Catanese). For each such $n$ we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined over $\mathsf{Q}$.

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