Symplectic birational transformations of the plane

Details Symplectic birational transformations of the plane Symplectic birational transformations of the plane

2010-12-03

arxiv.org/abs/1012.0706v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We study the group of symplectic birational transformations of the plane. It is proved that this group is generated by $\mathrm{SL}(2,\mathbb{Z})$, the torus and a special map of order $5$, as it was conjectured by A. Usnich. Then we consider a special subgroup $H$, of finite type, defined over any field which admits a surjective morphism to the Thompson group of piecewise linear automorphisms of $\mathbb{Z}^2$. We prove that the presentation for this group conjectured by Usnich is correct.

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