SL2-ACTIONS ON AFFINE T-VARIETIES

A T-variety is a normal variety endowed with a regular action of the algebraic torus T. In the first part of this talk, we present a combinatorial description of rational affine T-varieties of complexity one. This description generalizes the usual description of ane toric varieties via polyhedral cones. Next, we give a criterion, in terms of this combinatorial language, as to when a T-variety X admits an SL2-action that is normalized by T. As an application, we obtain the well known classication of quasihomogeneous SL2-threefolds due to Popov.

This is a joint work with Ivan Arzhantsev.