Polyhedral divisors and SL_2-actions on affine T-varieties

Details Polyhedral divisors and SL_2-actions on affine T-varieties Polyhedral divisors and SL_2-actions on affine T-varieties

2011-05-23

arxiv.org/abs/1105.4494v2

Mathematics

Algebraic Geometry

25 pages. Comments from the referee included. To appear in the Michigan Mathematical Journal

Scientific paper

In this paper we classify SL_2-actions on normal affine T-varieties that are normalized by the torus T. This is done in terms of a combinatorial description of T-varieties given by Altmann and Hausen. The main ingredient is a generalization of Demazure's roots of the fan of a toric variety. As an application we give a description of special SL_2-actions on normal affine varieties. We also obtain, in our terms, the classification of quasihomogeneous SL_2-threefolds due to Popov.

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