On meromorphic functions defined by a differential system of order $1$

DOI10.24033/bsmf.2475zbMath1080.32011arXivmath/0605787OpenAlexW1631246426MaRDI QIDQ5314619

Tristan Torrelli

Publication date: 5 September 2005

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605787

zbMATH Keywords

\({\mathcal D}\)-modulesarrangements of hyperplanesfree divisorslogarithmic de Rham complexlogarithmic comparison theoremGerms of meromorphic functions

Mathematics Subject Classification ID

Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Complex surface and hypersurface singularities (32S25) de Rham cohomology and algebraic geometry (14F40)

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A criterion for the logarithmic differential operators to be generated by vector fields ⋮ Quasihomogeneity of isolated hypersurface singularities and logarithmic cohomology ⋮ Gröbner bases and logarithmic \(\mathcal D\)-modules. ⋮ Localization at hyperplane arrangements: combinatorics and \({\mathcal D}\)-modules ⋮ The Jacobian module, the Milnor fiber, and the \(D\)-module generated by \(f^s\) ⋮ Duality and comparison for logarithmic de Rham complexes with respect to free divisors. ⋮ Linear free divisors and the global logarithmic comparison theorem ⋮ Decomposition factors of D-modules on hyperplane configurations in general position ⋮ A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors

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