On the Cohomology of Discriminantal Arrangements and Orlik-solomon Algebras

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...

Gröbner and Diagonal Bases in Orlik-solomon Type Algebras

The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the OrlikSolomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, call...

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,...

Arrangements and Local Systems

We use stratified Morse theory to construct a complex to compute the cohomology of the complement of a hyperplane arrangement with coefficients in a complex rank one local system. The linearization of this complex is shown to be the Aomoto complex of the arrangement. Using this result, we establish the relationship between the cohomology support loci of the complement and the resonance varietie...

Cohomology of the Brieskorn-Orlik-Solomon algebras