Linearisation of finite Abelian subgroups of the Cremona group of the plane
By J. Blanc. 2006
51 citations recorded by the source corpus.
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 non-trivial 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 non-trivial 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aeb5779af98069c8bc71045f6c091232498c3407
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Degree growth of birational maps of the plane (2011, result): “The proof of this result follows from a study of possible minimal pairs, which is similar to the one made in [7] for finite abelian subgroups of Bir(P2) (see [7, Lemmas 3.”