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.

Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties

Abstract: One can deform the complex structure of Calabi-Yau hypersurfaces in toric varieties by changing the coefficients of the defining polynomial. However, there must also exist non-polynomial deformations of the Calabi-Yau hypersurfaces which cannot be realized inside the ambient toric variety. In this paper, we have constructed the missing non-polynomial deformations, which are induced by an automorphism on the open part of the ambient toric variety.

Toric partial orders

Abstract: Toric partial orders correspond to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets arise from finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. There are natural toric analogues of many standard features of ordinary partial orders, such as chains, antichains, intervals, transitivity, Hasse diagrams, linear extensions, total orders, morphisms, and order ideals. Most of these only become apparent when one looks at these objects geometrically. Toric posets arise naturally in a wide variety of contexts, from the study of cyclic reducibility and conjugacy in Coxeter groups, to the critical path method (CPM) for scheduling activities with periodicity in operations research. This talk will be a survey on toric posets and it will be filled with lots of colorful pictures. This is joint work with Mike Develin and Vic Reiner.

Topological toric manifolds

Abstract: We introduce the notion of a topological toric manifold and a topological fan and show that there is a bijection between omnioriented topological toric manifolds and complete non-singular topological fans. A topological toric manifold is a topological analogue of a toric manifold and the family of topological toric manifolds is much larger than that of toric manifolds. A topological fan is a combinatorial object generalizing the notion of a simplicial fan in toric geometry. Prior to this paper, two topological analogues of a toric manifold have been introduced. One is a quasitoric manifold and the other is a torus manifold. One major difference between the previous notions and topological toric manifolds is that the former support a smooth action of an $S^1$-torus while the latter support a smooth action of a $\C^*$-torus. We also discuss their relation in details.