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Israel Journal of Mathematics

, Volume 182, Issue 1, pp 481–504 | Cite as

Torus invariant divisors

  • Lars PetersenEmail author
  • Hendrik Süss
Article

Abstract

Using the language of Altmann, Hausen and Süß, 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.

Keywords

Line Bundle Prime Divisor Global Section Torus Action Cartier Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Institut für Mathematik und InformatikFreie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, LS Algebra und GeometrieBrandenburgische Technische Universität CottbusCottbusGermany

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