Blanc, Jeremy. (2009) Linearisation of finite Abelian subgroups of the Cremona group of the plane. Groups, geometry and dynamics, Vol. 3, H. 2. pp. 215266.
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Official URL: http://edoc.unibas.ch/dok/A5843079
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Abstract
Given a finite Abelian subgroup of the Cremona group of the plane, we provide a way to decide whether it is birationally conjugate to a group of automorphisms of a minimal surface. In particular, we prove that a finite cyclic group of birational transformations of the plane is linearisable if and only if none of its nontrivial elements fix a curve of positive genus. For finite Abelian groups, there exists only one surprising exception, a group isomorphic to Z/2Z xZ/4Z, whose nontrivial elements do not fix a curve of positive genus but which is not conjugate to a group of automorphisms of a minimal rational surface. We also give some descriptions of automorphisms (not necessarily of finite order) of del Pezzo surfaces and conic bundles.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc) 

UniBasel Contributors:  Blanc, Jérémy 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  EMS Publishing House 
Note:  Publication type according to Uni Basel Research Database: Journal article 
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Last Modified:  04 Sep 2015 14:31 
Deposited On:  08 Jun 2012 06:47 
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