Related papers: Toric vector bundles and parliaments of polytopes

A toric vector bundle $\mathcal{E}$ is a torus equivariant vector bundle on a toric variety. We give a valuation theoretic and tropical point of view on toric vector bundles. We present three (equivalent) classifications of toric vector…

Jet ampleness of line bundles generalizes very ampleness by requiring the existence of enough global sections to separate not just points and tangent vectors, but also their higher order analogues called jets. We give sharp bounds…

We introduce a notion of tropical vector bundle on a tropical toric variety which is a tropical analogue of a torus equivariant vector bundle on a toric variety. Alternatively it can be called a toric matroid bundle. We define equivariant…

The goal of this paper is to introduce a construction of a vector bundle on a tropical variety. When the base is a tropical toric variety these tropicalize toric vector bundles, and are described by the data of a valuated matroid and some…

We associate to each toric vector bundle on a toric variety X(Delta) a "branched cover" of the fan Delta together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric…

In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides with the Kac polynomials of supernova quivers, which arise in the study of the moduli spaces of certain irregular…

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…

We show that an equivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a…

We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maximal rank. As an application, we construct a lattice polytope…

In this article we study covering spaces of symplectic toric orbifolds and symplectic toric orbifold bundles. In particular, we show that all symplectic toric orbifold coverings are quotients of some symplectic toric orbifold by a finite…

In this article we prove, in a simple way, that for any complete toric variety, and for any Cartier divisor, the ring of global sections of multiples of the line bundle associated to the divisor is finitely generated.

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…

We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to…

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this thesis we explore this correspondence to classify smooth lattice…

The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric…

Using the notion of a valuation into the semifield of piecewise linear functions, we give a classification of torus equivariant flat families of finite type over a toric variety base, by certain piecewise linear maps between fans. As a…

In this paper, using Klyachko's classification theorem we study positivity and semi-stability of toric vector bundles on a class of nonsingular projective toric varieties, known as Bott towers. In particular, we give a criterion of $s$-jet…

This paper studies two related subjects. One is some combinatorics arising from linear projections of polytopes and fans of cones. The other is quotient varieties of toric varieties. The relation is that projections of polytopes are related…

We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.