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ISSN 1079-6762

 

Nonrational, nonsimple convex polytopes in symplectic geometry


Authors: Fiammetta Battaglia and Elisa Prato
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 29-34
MSC (2000): Primary 53D05; Secondary 53D20, 32S60, 52B20
Published electronically: September 17, 2002
MathSciNet review: 1928499
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Abstract: 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.


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Additional Information

Fiammetta Battaglia
Affiliation: Dipartimento di Matematica Applicata “G. Sansone”, Via S. Marta 3, 50139 Firenze, Italy
Email: fiamma@dma.unifi.it

Elisa Prato
Affiliation: Laboratoire Dieudonné, Université de Nice, Parc Valrose, 06108 Nice Cedex 2, France
Email: elisa@alum.mit.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-02-00101-4
PII: S 1079-6762(02)00101-4
Keywords: Symplectic quasifolds, moment mapping, stratified spaces, convex polytopes
Received by editor(s): June 16, 2002
Published electronically: September 17, 2002
Additional Notes: The first author was partially supported by MIUR project Proprietà Geometriche delle Varietà Reali e Complesse, by GNSAGA (CNR), and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101).
Communicated by: Frances Kirwan
Article copyright: © Copyright 2002 American Mathematical Society