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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, Wang et al. showed that any convex simple lattice polytope is the moment polynomial of a Kahler-Ricci soliton on any toric monotone manifold.
Abstract: We show that any compact convex simple lattice polytope is the moment polytope of a Kahler–Einstein orbifold, unique up to orbifold covering and homothety. We extend the Wang–Zhu Theorem (Wang and Zhu in Adv Math 188:47–103, 2004) giving the existence of a Kahler–Ricci soliton on any toric monotone manifold on any compact convex simple labeled polytope satisfying the combinatoric condition corresponding to monotonicity. We obtain that any compact convex simple polytope Open image in new window admits a set of inward normals, unique up to dilatation, such that there exists a symplectic potential satisfying the Guillemin boundary condition (with respect to these normals) and the Kahler–Einstein equation on Open image in new window. We interpret our result in terms of existence of singular Kahler–Einstein metrics on toric manifolds.
29 citations
01 Dec 2005
TL;DR: In this article, the authors describe all smooth complete toric threefolds of Picard number 5 with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than 5.
Abstract: We describe all of smooth complete toric threefolds of Picard number 5 with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than 5.
29 citations
TL;DR: The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal as discussed by the authors.
Abstract: The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like adding monomial ideals and the Segre product. We describe how to obtain generating sets of toric fiber products in non-zero codimension and discuss persistence of normality and primary decompositions under toric fiber products.
Several applications are discussed, including (a) the construction of Markov bases of hierarchical models in many new cases, (b) a new proof of the quartic generation of binary graph models associated to K 4-minor free graphs, and (c) the recursive computation of primary decompositions of conditional independence ideals.
29 citations
TL;DR: In this article, it was shown that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley Polytope if n⩾2d+1.
29 citations
TL;DR: In this article, a cell complex Δ in a real torus whose cells describe uniformly all maps in the minimal projective bimodule resolution of A is constructed for an example in dimension four arising from a tilting bundle on a smooth toric Fano.
29 citations