Topic
Toric variety
About: Toric variety is a research topic. Over the lifetime, 2630 publications have been published within this topic receiving 65604 citations. The topic is also known as: torus embedding.
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TL;DR: The Hard Lefschetz theorem is known to hold for intersection cohomology of the toric variety associated to a rational convex polytope, hence it is well defined even for nonrational polytopes when there is no variety associated with it as mentioned in this paper.
Abstract: The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a general polytope.
77 citations
TL;DR: In this paper, an inductive approach to classify toric Fano varieties is presented, where the authors present a classification of the toric threefold with at worst canonical singularities.
Abstract: An inductive approach to classifying toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.
76 citations
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TL;DR: In this paper, the authors give an introduction to tropical geometry and prove some results in tropical intersection theory and give a foundational account of intersection theory with proofs of new theorems relating it to classical intersection theory.
76 citations
TL;DR: A new way to use marked sequences to encode permutations is developed, which provides a transparent explanation of the unimodality of Eulerian numbers and their isotypic refinements.
75 citations
75 citations