Torus invariant divisors

Lars Petersen, Hendrik Suess

Research output: Contribution to journalArticlepeer-review

Abstract

Using the language of Altmann, Hausen and Su, we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture, X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one-dimensional faces of it. Furthermore, we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D (h) ) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.

Original languageEnglish
Pages (from-to)481-504
Number of pages24
JournalIsrael journal of mathematics
Volume182
Issue number1
DOIs
Publication statusPublished - Mar 2011

Keywords

  • GEOMETRY
  • VARIETIES
  • SURFACES

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