The moment map and line bundles over presymplectic toric manifolds

Yael Karshon, Susan Tolman

Research output: Contribution to journalArticlepeer-review


We apply symplectic methods in studying smooth toric varieties with a closed, invariant 2-form ω that may have degeneracies. Consider the push-forward of Liouville measure by the moment map. We show that it is a “twisted polytope” in t* which is determined by the winding numbers of a map Sn−1 → t* around points in t*. The index of an equivariant, holomorphic line-bundle with curvature ω is a virtual T-representation which can easily be read from this “twisted polytope”.

Original languageEnglish (US)
Pages (from-to)465-484
Number of pages20
JournalJournal of Differential Geometry
Issue number3
StatePublished - Nov 1993
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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