Convex Polytopes and Quasilattices from the Symplectic Viewpoint

Details Convex Polytopes and Quasilattices from the Symplectic Viewpoint Convex Polytopes and Quasilattices from the Symplectic Viewpoint

2003-06-13

arxiv.org/abs/math/0306217v3

Commun. Math. Phys, 269, 283-310 (2007)

Mathematics

Symplectic Geometry

LaTeX, 29 pages. Revised version: TITLE changed, reorganization of notations and exposition, added remarks and references

Scientific paper

10.1007/s00220-006-0130-1

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on $\R^k$ modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the action of an (infinite) discrete 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.

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