The moment map and line bundles over presymplectic toric manifolds. Karshon, Y. & Tolman, S. Journal of Differential Geometry, 38(3):465–484, 1993.
Paper doi abstract bibtex 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\textasciitilde —\textgreater t* around points in t* . The index of an equivariant, holomorphic line-bundle with curvature ω is a virtual Trepresentation which can easily be read from this "twisted polytope".
@article{karshon_moment_1993,
title = {The moment map and line bundles over presymplectic toric manifolds},
volume = {38},
issn = {0022-040X},
url = {http://projecteuclid.org/euclid.jdg/1214454478},
doi = {10.4310/jdg/1214454478},
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{\textasciitilde} —{\textgreater} t* around points in t* . The index of an equivariant, holomorphic line-bundle with curvature ω is a virtual Trepresentation which can easily be read from this "twisted polytope".},
language = {en},
number = {3},
urldate = {2019-08-07},
journal = {Journal of Differential Geometry},
author = {Karshon, Yael and Tolman, Susan},
year = {1993},
pages = {465--484}
}
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