Homological Properties of Orlik-solomon Algebras

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...

On the Cohomology of Discriminantal Arrangements and Orlik-solomon Algebras

We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in ...

Cohomology of the Brieskorn-Orlik-Solomon algebras

Diagonal Bases in Orlik-solomon Type Algebras

To encode an important property of the “no broken circuit bases” of the Orlik-Solomon-Terao algebras, András Szenes has introduced a particular type of bases, the so called “diagonal basis”. We prove that this definition extends naturally to a large class of algebras, the so called χ-algebras. Our definitions make also use of an “iterative residue formula” based on the matroidal operation of co...

A Note on the Orlik-Solomon Algebra

LetM =M(E) be a matroid on a linear ordered set E . The Orlik–Solomon Z-algebra OS(M) of M is the free exterior Z-algebra on E , modulo the ideal generated by the circuit boundaries. The Z-module OS(M) has a canonical basis called ‘no broken circuit basis’ and denoted nbc. Let eX = ∏ ei , ei ∈ X ⊂ E . We prove that when eX is expressed in the nbc basis, then all the coefficients are 0 or ±1. We...