Polyhedral divisors and SL_2-actions on affine T-varieties

Abstract

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.

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

References in corpus (1)

• Ga-actions of fiber type on affine T-varieties

Cited by in corpus (7)

• Lie algebras of vertical derivations on semiaffine varieties with torus actions
• On homogeneous locally nilpotent derivations of trinomial algebras
• On the automorphism group of non-necessarily normal affine toric varieties
• Homogeneous locally nilpotent derivations of non-factorial trinomial algebras
• Root subgroups on affine spherical varieties
• Commuting homogeneous locally nilpotent derivations
• Additive group actions on affine T-varieties of complexity one in arbitrary characteristic