Abstract
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 language | English (US) |
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Pages (from-to) | 465-484 |
Number of pages | 20 |
Journal | Journal of Differential Geometry |
Volume | 38 |
Issue number | 3 |
DOIs | |
State | Published - Nov 1993 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology