Generalizing the passage from a fan to a toric variety, we provide a combinatorial approach
to construct arbitrary effective torus actions on normal, algebraic varieties. Based on the …

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 …

Extending work of Klyachko and Perling, we develop a combinatorial description of pure
equivariant sheaves of any dimension on an arbitrary nonsingular toric variety X. Using …

Given a smooth toric variety XX, the action of the torus TT lifts to the moduli space MM of
stable sheaves on X X. Using the pioneering work of Klyacho, a fairly explicit combinatorial …

For an equivariant reflexive sheaf over a polarised toric variety, we study slope stability of its
reflexive pullback along a toric fibration. Examples of such fibrations include equivariant …

We give an explicit description of toric sheaves on the weighted projective plane $\mathbb
{P}(a, b, c) $ viewed as a toric Deligne-Mumford stack. The integers $(a, b, c) $ are not …

Using the theory of Klyachko filtrations for reflexive sheaves on toric varieties, we give a
description of toric foliations and their singularities in terms of combinatorial data. We extend …

In this paper, we consider ℤ r-graded modules on the Cl⁡(X)-graded Cox ring ℂ⁢[x 1,…, xr]
of a smooth complete toric variety X. Using the theory of Klyachko filtrations in the reflexive …

For an equivariant log pair $(X, D) $ where $ X $ is a normal toric variety and $ D $ a
reduced Weil divisor, we study slope-stability of the logarithmic tangent sheaf $\mathcal {T} …

In this paper, we introduce the notion of a Klyachko diagram for a monomial ideal I in a
certain multi-graded polynomial ring, namely the Cox ring R of a smooth complete toric …