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Linearisation of finite Abelian subgroups of the Cremona group of the plane
| Content Provider | Semantic Scholar |
|---|---|
| Author | Blanc, Jérémy |
| Copyright Year | 2006 |
| 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 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×Z/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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0704.0537v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/0704.0537v2.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Chromosome Deletion Description Genus Immunostimulating conjugate (antigen) Subgroup A Nepoviruses cell transformation |
| Content Type | Text |
| Resource Type | Article |
