Gorenstein Toric Fano Varieties
نویسنده
چکیده
We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatorial and geometrical properties of reflexive polytopes.
منابع مشابه
Toward the classification of higher-dimensional toric Fano varieties
The purpose of this paper is to give basic tools for the classification of nonsingular toric Fano varieties by means of the notions of primitive collections and primitive relations due to Batyrev. By using them we can easily deal with equivariant blow-ups and blow-downs, and get an easy criterion to determine whether a given nonsingular toric variety is a Fano variety or not. As applications of...
متن کاملComplete toric varieties with reductive automorphism group
We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism...
متن کاملTowards the Mirror Symmetry for Calabi-Yau Complete Intersections in Gorenstein Toric Fano Varieties
We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hypersurfaces.
متن کاملQ-factorial Gorenstein Toric Fano Varieties with Large Picard Number
In dimension d, Q-factorial Gorenstein toric Fano varieties with Picard number ρX correspond to simplicial reflexive polytopes with ρX+d vertices. Casagrande showed that any d-dimensional simplicial reflexive polytope has at most 3d vertices, if d is even, respectively, 3d − 1, if d is odd. Moreover, for d even there is up to unimodular equivalence only one such polytope with 3d vertices, corre...
متن کاملClassification of pseudo-symmetric simplicial reflexive polytopes
Gorenstein toric Fano varieties correspond to so called reflexive polytopes. If such a polytope contains a centrally symmetric pair of facets, we call the polytope, respectively the toric variety, pseudo-symmetric. Here we present a complete classification of pseudo-symmetric simplicial reflexive polytopes. This is a generalization of a result of Ewald on pseudosymmetric nonsingular toric Fano ...
متن کامل