Nonrational, nonsimple convex polytopes in symplectic geometry

Details Nonrational, nonsimple convex polytopes in symplectic geometry Nonrational, nonsimple convex polytopes in symplectic geometry

2002-06-15

arxiv.org/abs/math/0206149v1

Electron. Res. Announc. Amer. Math. Soc., 8 (2002) 29-34.

Mathematics

Symplectic Geometry

LaTeX, 7 pages

Scientific paper

In this research announcement we associate to each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. the strata are locally modelled by $\R^k$ modulo the action of a discrete, possibly infinite, group. Each stratified space is endowed with a symplectic structure and a moment mapping having the property that its image gives the original polytope back. These spaces may be viewed as a natural generalization of symplectic toric varieties to the nonrational setting. We provide here the explicit construction of these spaces, and a thorough description of the stratification.

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