Nonrational, nonsimple convex polytopes in symplectic geometry
Authors:
Fiammetta Battaglia and Elisa Prato
Journal:
Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 2934
MSC (2000):
Primary 53D05; Secondary 53D20, 32S60, 52B20
Published electronically:
September 17, 2002
MathSciNet review:
1928499
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
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 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/S1079676202001014
PII:
S 10796762(02)001014
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. HPRNCT200000101).
Communicated by:
Frances Kirwan
Article copyright:
© Copyright 2002
American Mathematical Society
