A vanishing theorem for a class of logarithmic D-modules
| dc.creator | Castro-Jimenez, F. J. | |
| dc.creator | Gago, J. | |
| dc.creator | Hartillo-Hermoso, M. I. | |
| dc.creator | Ucha, J. M. | |
| dc.date | 2007-07-06 | |
| dc.date.accessioned | 2026-07-07T08:14:20Z | |
| dc.date.available | 2026-07-07T08:14:20Z | |
| dc.description | Let $O_X$ (resp. $D_X$) 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 $1/f^k$ over $D_X$ 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 $D_X$--module with $O_X$. The logarithmic $D_X$--module is naturally associated with $Y$. This result is related to the so called Logarithmic Comparison Theorem. | |
| dc.description | 13 pages. To appear in Revista Matemática Iberoamericana | |
| dc.identifier | https://arxiv.org/abs/0707.1000 | |
| dc.identifier | http://arxiv.org/abs/0707.1000 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133089 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32C20 (14F10, 32S40, 13P10) | |
| dc.title | A vanishing theorem for a class of logarithmic D-modules | |
| dc.type | text |