Report
Linearisation of finite abelian subgroups of the Cremona group of the plane
| العنوان: | Linearisation of finite abelian subgroups of the Cremona group of the plane |
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| المؤلفون: | Blanc, Jérémy |
| المصدر: | Groups Geom. Dyn. 3 (2009), no. 2, 215-266 |
| سنة النشر: | 2007 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14E07, 14E05, 14J26 |
| الوصف: | This article gives the proof of results announced in [J. Blanc, Finite Abelian subgroups of the Cremona group of the plane, C.R. Acad. Sci. Paris, S\'er. I 344 (2007), 21-26.] and some description of automorphisms of rational surfaces. 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/2ZxZ/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. Comment: 41 pages, 2 figures, is a part of the author's PHD whose full text is available at math.AG/0610368. To appear in Groups Geom. Dyn |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.4171/GGD/55 |
| URL الوصول: | http://arxiv.org/abs/0704.0537 |
| رقم الانضمام: | edsarx.0704.0537 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.4171/GGD/55 |
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