Lattice polytopes and toric varieties Master ’ s thesis ,
نویسندگان
چکیده
orbit closure, 32 character, 33cone, 9dual, 10lattice, 10strongly convex, 10convex function, 42 distinguished point, 28divisorCartier, 38T -invariant, 40principal, 39prime, 37Weil, 37T -invariant, 39principal, 38divisor class group, 38
منابع مشابه
Classification 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 ...
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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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P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and Pukhlikov [8] (valid for lattice polytopes such that the primitive vectors on edges through each vertex of P form a basis of the lattice). As a corollary, we recover results of Pommersheim [9] and ...
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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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We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes whose Minkowski sums are cut out by root systems. The proofs are based on a combinatorial characterization of diagonally split toric varieties.
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