2002/06/15 by Fiammetta Battaglia, Elisa Prato
Mathematics · #math.SG #math.AG #msc:53D05 #msc:53D20 #msc:32S60 #msc:52B20
published as Electron. Res. Announc. Amer. Math. Soc., 8 (2002) 29-34. · LaTeX, 7 pages
arxiv created 2002/06/15 · arxiv updated 2009/11/30
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 \Rk 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.