Cohomology of the Brieskorn-Orlik-Solomon algebras
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منابع مشابه
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 ...
متن کاملGröbner 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...
متن کاملArrangements 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,...
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Let AC = {H1, . . . , Hn} be a (central) arrangement of hyperplanes in C. Let M(AC) be the dependence matroid of the linear forms {θHi ∈ (C ) : Ker(θHi ) = Hi}. The Orlik-Solomon algebra OS(M) of a matroid M is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The algebra OS(M(AC)) is isomorphic to the cohomology algebra of the manifold M = C \ ⋃ H∈AC H. The T...
متن کاملOn 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...
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