Relative cohomology of bi-arrangements

Cohomology rings of arrangements

Arrangements and Cohomology

To a matroid M is associated a graded commutative algebra A A M , the OrlikSolomon algebra of M. Motivated by its role in the construction of generalized hypergeometric functions, we study the cohomology H A dω of A M with coboundary map dω given by multiplication by a fixed element ω of A1. Using a description of decomposable relations in A, we construct new examples of “resonant” values of ω,...

On Cohomology Algebras of Complex Subspace Arrangements

The integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement. We give a combinatorial presentation of the cohomology algebra in the spirit of the Orlik-Solomon result on the cohomology algebras of complex hyperplane arrangements. Our methods are elementary: we work wit...

The integer cohomology of toric Weyl arrangements

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper we prove that if T W̃ is the toric arrangement defined by the cocharacters lattice of a Weyl group W̃ , then the integer cohomology of its complement is torsion free.

Cohomology Algebras of Complex Subspace Arrangements 3