Generalized toric varieties for simple non-rational convex polytopes
| dc.creator | Battaglia, Fiammetta | |
| dc.creator | Prato, Elisa | |
| dc.date | 2000-04-11 | |
| dc.date | 2001-06-01 | |
| dc.date.accessioned | 2026-07-07T04:34:42Z | |
| dc.date.available | 2026-07-07T04:34:42Z | |
| dc.description | We call complex quasifold of dimension k a space that is locally isomorphic to the quotient of an open subset of the space C^k by the holomorphic action of a discrete group; the analogue of a complex torus in this setting is called a complex quasitorus. We associate to each simple polytope, rational or not, a family of complex quasifolds having same dimension as the polytope, each containing a dense open orbit for the action of a suitable complex quasitorus. We show that each of these spaces M is diffeomorphic to one of the symplectic quasifolds defined in http://arXiv.org/abs/math:SG/9904179, and that the induced symplectic structure is compatible with the complex one, thus defining on M the structure of a Kaehler quasifold. These spaces may be viewed as a generalization of the toric varieties that are usually associated to those simple convex polytopes that are rational. | |
| dc.description | LaTeX, 19 pages, some changes, final version to appear in Intern. Math. Res. Notices | |
| dc.identifier | https://arxiv.org/abs/math/0004066 | |
| dc.identifier | http://arxiv.org/abs/math/0004066 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59005 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | Generalized toric varieties for simple non-rational convex polytopes | |
| dc.type | text |