Delzant's theorem
In mathematics, Delzant's theorem, introduced by Thomas Delzant (1988), classifies effective Hamiltonian actions of a torus on a compact connected symplectic manifold of twice the dimension by their image under the momentum mapping (Delzant polytope). A Delzant polytope is a convex polytope in R^{n} such that the slopes of the edges of each vertex are given by a basis of Z^{n}.
As a corollary, these symplectic manifolds have a complex structure and can be promoted as toric varieties, with invariant Kähler structures.
References
- Delzant, Thomas (1988), "Hamiltoniens périodiques et images convexes de l'application moment", Bulletin de la Société Mathématique de France, 116 (3): 315–339, ISSN 0037-9484, MR 0984900
This Differential geometry related article is a stub. You can help Wikipedia by expanding it. |
This page is based on the copyrighted Wikipedia article "Delzant's theorem"; it is used under the Creative Commons
Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may
redistribute it, verbatim or modified, providing that you comply with
the terms of the CC-BY-SA