This paper is a continuation of our paper [HZ02] where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection between theâ€¦ (More)

The combinatorial structure of a d-dimensional simple convex polytope â€“ as given, for example, by the set of the (dâˆ’1)-regular subgraphs of the facets â€“ can be reconstructed from its abstract graph.â€¦ (More)

In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and p respectively i lattice points on the boundary respectively in the interior. The crucialâ€¦ (More)

Quasi-period collapse occurs when the Ehrhart quasi-polynomial of a rational polytope has a quasi-period less than the denominator of that polytope. This phenomenon is poorly understood, and allâ€¦ (More)

It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means ofâ€¦ (More)

The toric ideals of 3 Ã— 3 transportation polytopes Trc are quadratically generated. The only exception is the Birkhoff polytope B3. If Trc is not a multiple of B3, these ideals even have square-freeâ€¦ (More)

We discuss and give elementary proofs of results of Brion and of LawrenceVarchenko on the lattice-point enumerator generating functions for polytopes and cones. While this note is purely expository,â€¦ (More)