NORMAL SINGULARITIES WITH TORUS ACTIONS

Alvaro Liendo*, Hendrik Suess

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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, (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.

Original languageEnglish
Pages (from-to)105-130
Number of pages26
JournalTohoku mathematical journal
Volume65
Issue number1
Publication statusPublished - Mar 2013

Keywords

  • CONSTRUCTION
  • T-varieties
  • VARIETIES
  • RATIONAL SINGULARITIES
  • RINGS
  • toroidal desingularization
  • characterization of singularities
  • SURFACES
  • COMPLEXITY ONE
  • POLYHEDRAL DIVISORS
  • Torus actions

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