scispace - formally typeset
Search or ask a question
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
More filters
Journal ArticleDOI
TL;DR: This paper presents a precise geometric description of the variety associated to any tree on a Zariski open set, which contains all biologically meaningful points.
Abstract: In this paper we present geometric features of group based models. We focus on the 3-Kimura model. We present a precise geometric description of the variety associated to any tree on a Zariski open set. In particular this set contains all biologically meaningful points. Our motivation is a conjecture of Sturmfels and Sullivant on the degree in which the ideal associated to 3-Kimura model is generated.

15 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that if X is a toric scheme over a regular ring containing a field, then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant.
Abstract: We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic 0. The affine case of our result was conjectured by Gubeladze.

15 citations

Journal ArticleDOI
TL;DR: In this paper, a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles is given. But this work is restricted to the case of vector bundles.
Abstract: We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general description of equivariant sheaves on toric varieties. Here we give a first application of that description.

15 citations

Posted Content
TL;DR: The log-local principle of van Garrel-Graber-Ruddat conjectures that the genus 0 log Gromov-Witten theory of maximal tangency of $(X,D)$ is equivalent to the genus ε-local GA of the projective toric complex variety as mentioned in this paper.
Abstract: Let $X$ be a smooth projective complex variety and let $D=D_1+\cdots+D_l$ be a reduced normal crossing divisor on $X$ with each component $D_j$ smooth, irreducible, and nef. The log-local principle of van Garrel-Graber-Ruddat conjectures that the genus 0 log Gromov-Witten theory of maximal tangency of $(X,D)$ is equivalent to the genus 0 local Gromov-Witten theory of $X$ twisted by $\bigoplus_{j=1}^l\mathcal{O}(-D_j)$. We prove that an extension of the log-local principle holds for $X$ a (not necessarily smooth) $\mathbb{Q}$-factorial projective toric variety, $D$ the toric boundary, and descendent point insertions.

15 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the generators of cluster variables for the quiver associated to the cone over the del Pezzo surface d P fixme 3 and provided an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the dP fixme 3 brane tiling.
Abstract: Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi–Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In combinatorial language, a brane tiling is a bipartite graph on a torus and its perfect matchings are of interest to both combinatorialists and physicists alike. A cluster algebra may also be associated to such quivers and in this paper we study the generators of this algebra, known as cluster variables, for the quiver associated to the cone over the del Pezzo surface d P 3. In particular, mutation sequences involving mutations exclusively at vertices with two in-coming arrows and two out-going arrows are referred to as toric cascades in the string theory literature. Such toric cascades give rise to interesting discrete integrable systems on the level of cluster variable dynamics. We provide an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the d P 3 brane tiling for these formulas in most cases.

15 citations


Network Information
Related Topics (5)
Cohomology
21.5K papers, 389.8K citations
96% related
Moduli space
15.9K papers, 410.7K citations
95% related
Conjecture
24.3K papers, 366K citations
92% related
Abelian group
30.1K papers, 409.4K citations
92% related
Lie algebra
20.7K papers, 347.3K citations
90% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202346
2022112
2021107
2020107
2019100
201894