Abstract. 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. If we restrict to the rational case we obtain, from the point of view of singularities, what is expected from the classical theory of toric varieties, and in addition we gain further insight on the symplectic geometry of them; it should also be noticed that these spaces provide a wide range of explicit examples of symplectic stratified spaces. Communicated by A. Connes. Partially supported by GNSAGA (CNR). Received: 5 May 2005/Accepted: 5 May 2006. Published online: 4 November 2006.
Convex Polytopes and Quasilattices from the Symplectic Viewpoint / F. BATTAGLIA. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 269:(2007), pp. 283-310. [10.1007/s00220-006-0130-1]
Convex Polytopes and Quasilattices from the Symplectic Viewpoint
BATTAGLIA, FIAMMETTA
2007
Abstract
Abstract. 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. If we restrict to the rational case we obtain, from the point of view of singularities, what is expected from the classical theory of toric varieties, and in addition we gain further insight on the symplectic geometry of them; it should also be noticed that these spaces provide a wide range of explicit examples of symplectic stratified spaces. Communicated by A. Connes. Partially supported by GNSAGA (CNR). Received: 5 May 2005/Accepted: 5 May 2006. Published online: 4 November 2006.File | Dimensione | Formato | |
---|---|---|---|
ns-sympl-abstract.pdf
accesso aperto
Tipologia:
Altro
Licenza:
Open Access
Dimensione
37.5 kB
Formato
Adobe PDF
|
37.5 kB | Adobe PDF | |
nonsimple-symplectic.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
354.92 kB
Formato
Adobe PDF
|
354.92 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.