Related papers: Equivariant stable sheaves and toric GIT

We investigate the tilt-stability of stable sheaves on projective varieties with respect to certain tilt-stability conditions depends on two parameters constructed by Bridgeland. For a stable sheaf, we give effective bounds of these…

Extending work of Klyachko, Perling and Kool we develop a combinatorial description of torsion free toric sheaves in any dimension on smooth toric DM stacks. We investigate their basic properties and under certain conditions recover some…

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…

In this paper we construct full support character sheaves for stably graded Lie algebras. Conjecturally these are precisely the cuspidal character sheaves. Irreducible representations of Hecke algebras associated to complex reflection…

We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate…

For $G$ an algebraic group definable over a model of $\operatorname{ACVF}$, or more generally a definable subgroup of an algebraic group, we study the stable completion $\widehat{G}$ of $G$, as introduced by Loeser and the second author.…

We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra…

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…

Let $(X, \Delta)$ be a log Fano pair with standard coefficients endowed with a singular K\"ahler--Einstein metric. We show that the adapted tangent sheaf $\mathcal{T}_{X, \Delta, f}$ and the adapted canonical extension $\mathcal{E}_{X,…

The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stability on a piecewise hereditary triangulated…

We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are then applied to the…

Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We…

We give a conjectural but full and explicit description of the (K-theoretic) equivariant vertex for Pandharipande--Thomas stable pairs on toric Calabi--Yau 4-folds, by identifying torus-fixed loci as certain quiver Grassmannians and…

We give a classification of the equivariant principal $G$-bundles on a nonsingular toric variety when $G$ is a closed Abelian subgroup of $GL_k(\mathbb{C})$. We prove that any such bundle splits, that is, admits a reduction of structure…

If G is a reductive group which acts on a linearized smooth scheme $X$ then we show that under suitable standard conditions the derived category of coherent sheaves of the corresponding GIT quotient stack $X^{ss}/G$ has a semi-orthogonal…

Let S be a smooth projective surface, K be the canonical class of S and H be an ample divisor such that H.K<0 . In this paper we prove that for any rigid (Ext^1(F,F)=0) semistable sheaf F in the sense of Mumford--Takemoto stability w.r.t. H…

We construct the derived scheme of stable sheaves on a smooth projective variety via derived moduli of finite graded modules over a graded ring. We do this by dividing the derived scheme of actions of Ciocan-Fontanine and Kapranov by a…

Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally…

Let $M$ be a smooth complex projective toric variety equipped with an action of a torus $T$, such that the complement $D$ of the open $T$--orbit in $M$ is a simple normal crossing divisor. Let $G$ be a complex reductive affine algebraic…

Let $K$ be a complete discrete valuation field whose residue field is perfect and of positive characteristic, let $X$ be a connected, proper scheme over $\mathcal{O}_K$, and let $U$ be the complement in $X$ of a divisor with simple normal…