2009/09/23 by Alvaro Liendo, Liendo, Alvaro
Computer Science · Mathematics · #Affine transformation #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic geometry #Algebraic number #Algebraic variety #Commutative Algebra and Its Applications #Geometry #Gravitational singularity #Mathematical analysis #Mathematics #Polynomial and algebraic computation #Pure mathematics #Sheaf #Singular point of an algebraic variety #Toric variety #Torus #Variety (cybernetics) #math.AG #msc:14E15. #msc:14J17
paper · pdf · doi:10.48550/arxiv.0909.4134
12 p
arxiv created 2009/09/23 · openalex publication_date 2009/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.