Linear free divisors and the global logarithmic comparison theorem

DOI10.5802/aif.2448zbMath1163.32014arXivmath/0607045OpenAlexW1630952934MaRDI QIDQ1013032

Michel Granger, Alicia Nieto-Reyes, Mathias Schulze, D. M. Q. Mond

Publication date: 29 April 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607045

zbMATH Keywords

de Rham cohomologyLie algebra cohomologyfree divisorprehomogeneous vector spacequiver representationlogarithmic comparison theorem

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) de Rham cohomology and algebraic geometry (14F40) Global theory of complex singularities; cohomological properties (32S20) Cohomology theory for linear algebraic groups (20G10)

Related Items (21)

Hodge ideals of free divisors ⋮ Lifting free divisors ⋮ Homological properties of determinantal arrangements ⋮ Local cohomology of logarithmic forms ⋮ Combinatorially determined zeroes of Bernstein--Sato ideals for tame and free arrangements ⋮ Triple root systems, rational quivers and examples of linear free divisors ⋮ Duality of Gauß-Manin systems associated to linear free divisors ⋮ Solvable groups, free divisors and nonisolated matrix singularities. II: Vanishing topology ⋮ Solvable group representations and free divisors whose complements are \(K(\pi,1)\)'s ⋮ Syzygies and logarithmic vector fields along plane curves ⋮ Constructions and classifications of projective Poisson varieties ⋮ The Jacobian module, the Milnor fiber, and the \(D\)-module generated by \(f^s\) ⋮ Bernstein polynomials and spectral numbers for linear free divisors ⋮ Deformations of free and linear free divisors ⋮ Linear free divisors and the global logarithmic comparison theorem ⋮ Solvable groups, free divisors and nonisolated matrix singularities. I: Towers of free divisors ⋮ Topology of exceptional orbit hypersurfaces of prehomogeneous spaces ⋮ Linear free divisors and Frobenius manifolds ⋮ Tautological systems and free divisors ⋮ A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors ⋮ Noncommutative (crepant) desingularizations and the global spectrum of commutative rings

Cites Work

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• Semi-Invariants of Quivers
• A classification of irreducible prehomogeneous vector spaces and their relative invariants
• Logarithmic Comparison Theorem and some Euler homogeneous free divisors
• Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements
• Cohomology of the complement of a free divisor
• On meromorphic functions defined by a differential system of order $1$
• On the formal structure of logarithmic vector fields
• On the De Rham cohomology of algebraic varieties
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