Normal singularities with torus actions
arXiv:1005.2462 · doi:10.2748/tmj/1365452628
Abstract
We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (QQ-)factorial, or (QQ-)Gorenstein singularities. We also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally, we provide a method to construct factorial affine varieties with a torus action. This leads to a full classification of such varieties in the case where the action is of complexity one.
23 pages
References in corpus (4)
Cited by in corpus (23)
- K-semistability is equivariant volume minimization
- Algebraicity of the Metric Tangent Cones and Equivariant K-stability
- Ga-actions of fiber type on affine T-varieties
- K-Stability for Fano Manifolds with Torus Action of Complexity One
- Log terminal singularities, platonic tuples and iteration of Cox rings
- Non-complete rational T-varieties of complexity one
- On terminal Fano 3-folds with 2-torus action
- Kahler-Einstein metrics on symmetric Fano T-varieties
- On Generalized Wronskians
- The Geometry of T-Varieties
- Holography, Matrix Factorizations and K-stability
- Stringy invariants for horospherical varieties of complexity one
- Stability of Valuations: Higher Rational Rank
- Smooth projective varieties with a torus action of complexity 1 and Picard number 2
- Exceptional Sequences on Rational C*-Surfaces
- Iteration of Cox rings of klt singularities
- A geometric characterization of toric singularities
- Reductive quotients of klt singularities
- Cox rings of rational complexity one T-varieties
- Cox rings of almost homogeneous SL2-threefolds
- On irregular Sasaki-Einstein metrics in dimension 5
- Fano threefolds with 2-torus action - a picture book
- Flexible affine cones and flexible coverings