The tropical momentum map: a classification of toric log symplectic manifolds

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization of affine space called a log affine manifold. Using this momentum map, we obtain a complete classification of such manifolds in terms of decorated log affine polytopes, hence extending the classification of symplectic toric manifolds achieved by Atiyah, Guillemin-Sternberg, Kostant, and Delzant.


Published in:
Mathematische Annalen, 367, 3-4, 1217-1258
Year:
2017
Publisher:
Heidelberg, Springer Verlag
ISSN:
0025-5831
Laboratories:




 Record created 2017-05-01, last modified 2018-09-13


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