Cohomology of the brieskorn-orlik-solomon algebras

DOI10.1080/00927879508825535zbMath0851.32027OpenAlexW2002673001MaRDI QIDQ4863789

Sergey Yuzvinsky

Publication date: 28 November 1996

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879508825535

zbMATH Keywords

deRham cohomologyhyperplane arrangementlocal systemvanishing of cohomology groupsBrieskorn-Orlik-Solomon algebra

Mathematics Subject Classification ID

Analytic sheaves and cohomology groups (32C35) de Rham cohomology and algebraic geometry (14F40) Vanishing theorems (32L20)

Related Items (27)

FUNCTIONAL IDENTITIES REVISED: THE FRACTIONAL AND THE STRONG DEGREE ⋮ Vanishing results for the Aomoto complex of real hyperplane arrangements via minimality ⋮ Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors ⋮ The equivariant Kazhdan-Lusztig polynomial of a matroid ⋮ Homology of iterated semidirect products of free groups ⋮ Chen ranks and resonance ⋮ Non-vanishing of the twisted cohomology on the complement of hypersurfaces ⋮ Nets in \(\mathbb{P}^2\) and Alexander duality ⋮ Higher Resonance Varieties of Matroids ⋮ Higher Topological Complexity of Artin Type Groups ⋮ Nonresonance conditions for arrangements. ⋮ Double coverings of arrangement complements and 2-torsion in Milnor fiber homology ⋮ 𝛽𝐧𝐛𝐜-bases for cohomology of local systems on hyperplane complements ⋮ The non-vanishing cohomology of Orlik-Solomon algebras ⋮ Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equations ⋮ The Dimension of the Cohomology Groups of the Orlik–Solomon Algebras ⋮ Vanishing and bases for cohomology of partially trivial local systems on hyperplane arrangements ⋮ Combinatorial and algebraic structure in Orlik-Solomon algebras ⋮ Arrangements and Frobenius like structures ⋮ The combinatorial Laplacian of the Tutte complex ⋮ Hyperplane arrangement cohomology and monomials in the exterior algebra ⋮ The Orlik-Solomon complex and Milnor fibre homology ⋮ On the monodromy action on Milnor fibers of graphic arrangements ⋮ Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence ⋮ Efficient computation of resonance varieties via Grassmannians ⋮ Arrangements and cohomology ⋮ Hypergeometric integrals and arrangements

Cites Work

• On geometric semilattices
• Homology of a local system on the complement of hyperplanes
• Cohen-Macaulay rings of sections
• Combinatorics and topology of complements of hyperplanes
• Arrangements of hyperplanes and Lie algebra homology
• Whitney numbers of geometric lattices
• Cohomology of local systems on the complement of hyperplanes
• Logarithmic forms on affine arrangements
• A higher invariant for matroids

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