Related papers: The hypertoric intersection cohomology ring

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic…

Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…

Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no…

We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section space of a projective bundle, and show that it induces an…

We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal representation, to computations involving line bundles, making them…

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are…

We describe the relationship between intersection cohomology with twisted coefficients and the perverse sheaves which play the role of the eigenspaces for the Milnor monodromy of an affine hypersurface.

Hypertoric varieties are hyperk\"ahler analogues of toric varieties, and are constructed as abelian hyperk\"ahler quotients of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold…

This paper continues the development of the deformation theory of abelian categories introduced in a previous paper by the authors. We show first that the deformation theory of abelian categories is controlled by an obstruction theory in…

Let $C$ be a smooth projective curve, $E$ a locally free sheaf. Hyperquot schemes on $C$ parametrise flags of coherent quotients of $E$ with fixed Hilbert polynomial, and offer alternative compactifications to the spaces of maps from $C$ to…

Motivated by problems in which data are given over covering generating families, we suggest a new cohomology theory for diffeological spaces, called diffeological \v{C}ech cohomology, which is an exact $ \partial $-functor of the section…

We establish the relationship between the cohomology of a certain sheaf on the intersection lattice of a hyperplane arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf on punctured affine space, respectively…

Over a smooth projective toric variety we study toric sheaves, that is, reflexive sheaves equivariant with respect to the acting torus, from a polyhedral point of view. One application is the explicit construction of the torus invariant…

We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise…

This paper addresses the problem of constructing a cycle-level intersection theory for toric varieties. We show that by making one global choice, we can determine a cycle representative for the intersection of an equivariant Cartier divisor…

Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. "toric varieties over arbitrary base rings". It is shown how the base ring affects the geometry of a toric scheme. Moreover, generalisations of…

We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can…

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes. A quasi-coherent sheaf on X gives rise, by taking sections over the covering sets, to a diagram of modules over the various coordinate rings. The resulting…

We study moduli spaces of twisted quasimaps to a hypertoric variety $X$, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are…

Given a quasi-compact, quasi-separated scheme X, a bijection between the tensor localizing subcategories of finite type in Qcoh(X) and the set of all subsets $Y\subseteq X$ of the form $Y=\bigcup_{i\in\Omega}Y_i$, with $X\setminus Y_i$…