Generalized toric varieties for simple non-rational convex polytopes

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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.
LaTeX, 19 pages, some changes, final version to appear in Intern. Math. Res. Notices

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Complex Variables, Algebraic Geometry, Combinatorics, Differential Geometry, Symplectic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/59005

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0004066
 http://arxiv.org/abs/math/0004066

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arXiv