Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence

DOI10.1090/S0002-9947-05-03853-5zbMath1153.52008arXivmath/0502438MaRDI QIDQ3372164

Henry K. Schenck, Alexander I. Suciu

Publication date: 17 February 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502438

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Syzygies, resolutions, complexes in associative algebras (16E05)

Related Items

Homological properties of Orlik-Solomon algebras, Open problems on syzygies and Hilbert functions, Mini-workshop: Cohomology rings and fundamental groups of hyperplane arrangements, wonderful compactifications, and real toric varieties. Abstracts from the mini-workshop held September 30 -- October 6, 2012., Topological invariants of groups and Koszul modules, On the homotopy Lie algebra of an arrangement, Chen ranks and resonance, Nets in \(\mathbb{P}^2\) and Alexander duality, Universally Koszul and initially Koszul properties of Orlik–Solomon algebras, Efficient computation of resonance varieties via Grassmannians

Uses Software

• Macaulay2
• BGG

Cites Work

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• BGG
• Annihilators of Orlik-Solomon relations
• When does the associated graded Lie algebra of an arrangement group decompose?
• Combinatorics and topology of complements of hyperplanes
• Completion of link modules
• Arrangements and cohomology
• Un théorème du type de Matsushima-Murakami concernant l'intégrale des fonctions multiformes
• Arrangements and local systems
• Koszul homology and Lie algebras with application to generic forms and points
• Cohomology of local systems on the complement of hyperplanes
• Integration in free groups
• Orlik-Solomon algebras in algebra and topology
• Alexander invariants of complex hyperplane arrangements
• Characteristic varieties of arrangements
• Un théorème de Zariski du type de Lefschetz
• Hyperplane arrangement cohomology and monomials in the exterior algebra
• Sheaf cohomology and free resolutions over exterior algebras
• Hall invariants, homology of subgroups, and characteristic varieties
• Lower central series and free resolutions of hyperplane arrangements
• The Geometry of Syzygies
• Resolutions of monomial ideals and cohomology over exterior algebras
• Cohomology of the brieskorn-orlik-solomon algebras
• Chen Lie algebras
• Computational methods of commutative algebra and algebraic geometry. With chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman