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Article Dans Une Revue Electronic Research Announcements of the American Mathematical Society Année : 2002

Nonrational, nonsimple convex polytopes in symplectic geometry

Résumé

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.

Dates et versions

hal-00019449 , version 1 (21-02-2006)

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Fiammetta Battaglia, Elisa Prato. Nonrational, nonsimple convex polytopes in symplectic geometry. Electronic Research Announcements of the American Mathematical Society, 2002, 8, pp.29-34. ⟨hal-00019449⟩
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