Geodesic
Nonrational, nonsimple convex polytopes in symplectic geometry
Battaglia, Fiammetta1 ; Prato, Elisa2
1 Dipartimento di Matematica Applicata “G. Sansone”, Via S. Marta 3, 50139 Firenze, Italy
2 Laboratoire Dieudonné, Université de Nice, Parc Valrose, 06108 Nice Cedex 2, France
Electronic research announcements of the American Mathematical Society, Tome 08 (2002), pp. 29-34.

Voir la notice de l'article provenant de la source American Mathematical Society

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 modeled by ${\mathbb {R}}^k$ 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.
DOI : 10.1090/S1079-6762-02-00101-4

Battaglia, Fiammetta 1 ; Prato, Elisa 2

1 Dipartimento di Matematica Applicata “G. Sansone”, Via S. Marta 3, 50139 Firenze, Italy
2 Laboratoire Dieudonné, Université de Nice, Parc Valrose, 06108 Nice Cedex 2, France 
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Battaglia, Fiammetta; Prato, Elisa. Nonrational, nonsimple convex polytopes in symplectic geometry. Electronic research announcements of the American Mathematical Society, Tome 08 (2002), pp. 29-34. doi : 10.1090/S1079-6762-02-00101-4. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-02-00101-4/

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