2007/07/06 by F. J. Castro-Jimenez, Francisco Jesús Castro Jiménez, J. Gago +7
Computer Science · Mathematics · #13P10) #32C20 (14F10 #32S40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Matrix Theory and Algorithms #Rings, Modules, and Algebras #math.AG #msc:32C20 #msc:32S40
paper · pdf · doi:10.48550/arxiv.0707.1000
13 pages. To appear in Revista Matemática Iberoamericana
arxiv created 2007/07/06 · openalex publication_date 2007/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X (=the complex affine n-space). Let Y be a locally weakly quasi-homogeneous free divisor defined by a polynomial f. In this paper we prove that, locally, the annihilating ideal of 1/fk over DX is generated by linear differential operators of order 1 (for k big enough). For this purpose we prove a vanishing theorem for the extension groups of a certain logarithmic DX--module with OX. The logarithmic DX--module is naturally associated with Y. This result is related to the so called Logarithmic Comparison Theorem.