NORMAL SINGULARITIES WITH TORUS ACTIONS

By Alvaro Liendo, Hendrik Suss. 2010

61 citations recorded by the source corpus.

We propose a method to compute a desingularization of a normal affine varietyX 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, (Q-)factorial, or (Q-)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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8dc381b2901b12c610852688605700d7abe2d537

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In Algebra and Number Theory

1. Chi Li
2. Yuchen Liu

In Geometry and Topology

1. Yuchen Liu
2. Chi Li
3. H. Blum
4. Chenyang Xu
5. Ziquan Zhuang
6. Mattias Jonsson
7. Kento Fujita
8. Xiaowei Wang

Citations in the corpus

• A Guided Tour to Normalized Volume (2018, background): “u →D(u) is piecewisely linear; (3) D(u) is semiample for any u ∈σ∨, and D(u) is big if u is in the relative interior of σ∨. Here Y is projective since from our assumption H0(Y,OY ) = RT = R0 = C (see [LS13]). We collect some basic results about valuations on T-varieties. Theorem 3.5 (see [AIP+12]). ”