7 papers · 1 filter
On torsion in homology of singular toric varieties
Andrzej Weber
Let be a toric variety. Rationally Borel-Moore homology of is isomorphic to the homology of the Koszul complex $A^T_*(X)\otimes Λ^\x M$, where is the equivariant…
Pure homology of algebraic varieties
Andrzej Weber
We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically inv…
Weights in the cohomology of toric varieties
Andrzej Weber
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection…
Residue forms on singular hypersurfaces
Andrzej Weber
The purpose of this paper is to point out a relation between the canonical sheaf and the intersection complex of a singular algebraic variety. We focus on the hypersurface case. Le…
Formality of equivariant intersection cohomology
Andrzej Weber
We present several approaches to equivariant intersection cohomology. We show that for a complete algebraic variety acted by a connected algebraic group it is a free module ove…
Koszul Duality for modules over Lie algebra
Tomasz Maszczyk, Andrzej Weber
Let be a reductive Lie algebra over a field of characteristic zero. Suppose acts on a complex of vector spaces by and , which satisfy the identities as contr…