Toric Fano Varieties and Convex Polytopes
نویسنده
چکیده
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منابع مشابه
Fano Polytopes
Fano polytopes are the convex-geometric objects corresponding to toric Fano varieties. We give a brief survey of classification results for di↵erent classes of Fano polytopes.
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It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P ⊂ R of positive finite volume, such that P ⋂ Z consists of the point 0 and vertices of P (cf., e.g. [10], [36]). Likewise, Q−factorial terminal toric singularities essentially correspond to lattice simplexes with no lattice points inside or on the boundary (excep...
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We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
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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 combinatoria...
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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 ...
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Let us first recall our setting. In the toric case, there is a correspondence between n-dimensional nonsingular Fano varieties and ndimensional Fano polytopes, where the Fano varieties are biregular isomorphic if and only if the corresponding Fano polytopes are unimodularly equivalent. Here, given a lattice N of rank n, a Fano polytope Q ⊆ NR := N ⊗Z R is given as a lattice polytope containing ...
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