Rational singularities of normal T-varieties

Details Rational singularities of normal T-varieties Rational singularities of normal T-varieties

2009-09-23

arxiv.org/abs/0909.4134v1

Mathematics

Algebraic Geometry

12 p

Scientific paper

A T-variety is an algebraic variety X with an effective regular action of an algebraic torus T. Altmann and Hausen gave a combinatorial description of an affine T-variety X by means of polyhedral divisors. In this paper we compute the higher direct images of the structure sheaf of a desingularization of X in terms of this combinatorial data. As a consequence, we give a criterion as to when a T-variety has rational singularities. We also provide a partial criterion for a T-variety to be Cohen-Macaulay. As an application we characterize in this terms quasihomogeneous elliptic singularities of surfaces.

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