منابع مشابه
Reflexive Polytopes of Higher Index
We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive polygons via a change of the underlying lattice. This allows us to efficiently classify all isomorphism classes of l-reflexive polygons up to index 200. As another ...
متن کاملFlow polytopes and the graph of reflexive polytopes
We suggest defining the structure of an unoriented graph Rd on the set of reflexive polytopes of a fixed dimension d. The edges are induced by easy mutations of the polytopes to create the possibility of walks along connected components inside this graph. For this, we consider two types of mutations: Those provided by performing duality via nef-partitions, and those arising from varying the lat...
متن کاملLattices generated by skeletons of reflexive polytopes
Lattices generated by lattice points in skeletons of reflexive polytopes are essential in determining the fundamental group and integral cohomology of Calabi-Yau hypersurfaces. Here we prove that the lattice generated by all lattice points in a reflexive polytope is already generated by lattice points in codimension two faces. This answers a question of J. Morgan.
متن کاملReflexive Polytopes and Lattice-Polarized K3 Surfaces
We review the standard formulation of mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, and compare this construction to a description of mirror symmetry for K3 surfaces which relies on a sublattice of the Picard lattice. We then show how to combine information about the Picard group of a toric ambient space with data about automorphisms of the toric variety to identify families ...
متن کاملAn Ehrhart Series Formula For Reflexive Polytopes
It is well known that for P and Q lattice polytopes, the Ehrhart polynomial of P×Q satisfies LP×Q(t) = LP (t)LQ(t). We show that there is a similar multiplicative relationship between the Ehrhart series for P , for Q, and for the free sum P ⊕ Q that holds when P is reflexive and Q contains 0 in its interior. Let P be a lattice polytope of dimension d, i.e. a convex polytope in R whose vertices ...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2020
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-020-00199-8