Related papers: Intersection Cohomology of reductive varieties

A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics…

Type-A toric varieties may be obtained as GIT quotients with respect to a torus action with weights corresponding to roots of the group $SL(k)$ for some $k>1$. These varieties appear in various important applications, in particular, as…

The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus $\mathbb{T}$, one of our result determines the intersection cohomology Betti numbers of any normal…

We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.

We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties. As a consequence, we obtain the vanishing…

We present a proof of the algorithm for computing line bundle valued cohomology classes over toric varieties conjectured by R.~Blumenhagen, B.~Jurke and the authors (arXiv:1003.5217) and suggest a kind of Serre duality for combinatorial…

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…

We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our…

A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory.

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise).…

Every cohomology ring isomorphism between two non-singular complete toric varieties and quasitoric manifolds, respectively, with second Betti number $2$ is realizable by a diffeomorphism and homeomorphism, respectively.

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…

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…

This is an extended abstract for a talk given at the mini-workshop "Cohomology rings and fundamental groups of hyperplane arrangements, wonderful compactifications, and real toric varieties", held in Oberwolfach, September 30-October 6,…

In this paper we give a new characterization of the h-vector of the chromatic polynomial of a graph. We introduce reduced chromatic cohomology of a graph and show that h_i are its Betti numbers. We then discuss various combinatorial…

In this paper we construct a spectral sequence computing a modified version of morphic cohomology of a toric variety (even when it is singular) in terms of combinatorial data coming from the fan of the toric variety.

We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.

Given an affine toric variety $X$ embedded in a smooth variety, we prove a general result about the mixed Hodge module structure on the local cohomology sheaves of $X$. As a consequence, we prove that the singular cohomology of a proper…

In a paper by Lin an interesting family of semipermutations comes out to index the elements of a cohomology basis of a Hessenberg type variety. The corresponding Betti numbers are a generalization of Eulerian numbers. We show three…

We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to…