Related papers: Selected topics on Toric Varieties

We study the multi-height distribution of rational points of smooth, projective and split toric varieties over $\mathbf{Q}$ using the lift of the number of points to universal torsors.

We give a combinatorial description of the multiplicity at any torus fixed point on a Richardson variety in the Symplectic Grassmannian.

Given a smooth and projective curve C and a smooth and projective toric variety X, we first describe a compactification of the space of morphisms from C to X representing a fixed homology class, and after we study the intersection theory on…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…

Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…

The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…

We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under…

In this paper we describe the notion of a toric supervariety, generalizing that of a toric variety from the classical setting. We give a combinatorial interpretation of the category of quasinormal toric supervarieties with one odd dimension…

For a complete toric variety, we obtain an explicit formula for the localized equivariant Todd class in terms of the combinatorial data -- the fan. This is based on the equivariant Riemann-Roch theorem and the computation of the equivariant…

This article is based on my lecture notes from summer schools at the Universities of Utah (June 2007) and Warwick (September 2007). We provide an introduction to explicit methods in the study of moduli spaces of quiver representations and…

We first construct explicit bases for the cotangent spaces at singular points on Hibi toric varieties, i.e., toric varieties associated to distributive lattices. We then determine the singular loci of these toric varieties.

We describe a class of toric varieties in the $N$-dimensional affine space which are minimally defined by no less than $N-2$ binomial equations.

These notes survey some basic results in toric varieties over a field with examples and applications. A computer algebra package (written by the second author) is described which deals with both affine and projective toric varieties in any…

We study toric varieties over an arbitrary field with an emphasis on toric surfaces in the Merkurjev-Panin motivic category of "K-motives". We explore the decomposition of certain toric varieties as K-motives into products of central simple…

In this paper we explain four viewpoints on the local tropicalization of formal subgerms of toric germs, which is a local analog of the global tropicalization of subvarieties of algebraic tori. We start by illustrating some of those…

This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…

This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…

We prove that an open Richardson variety in the complete flag variety for $\mathrm{GL}_n$ is isomorphic to a torus if and only if the corresponding closed Richardson variety is toric. Such toric varieties can be classified in terms of the…

A toric variety is a normal complex variety which is completely described by combinatorial data, namely by a fan of strongly convex rational (with respect to a lattice) cones. Due to this rationality condition, toric varieties are…