An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation
| dc.creator | Oaku, Toshinori | |
| dc.creator | Takayama, Nobuki | |
| dc.date | 1998-01-26 | |
| dc.date.accessioned | 2026-07-07T05:23:40Z | |
| dc.date.available | 2026-07-07T05:23:40Z | |
| dc.description | We give an algorithm to compute the following cohomology groups on $U = \C^n \setminus V(f)$ for any non-zero polynomial $f \in \Q[x_1, ..., x_n]$; 1. $H^k(U, \C_U)$, $\C_U$ is the constant sheaf on $U$ with stalk $\C$. 2. $H^k(U, \Vsc)$, $\Vsc$ is a locally constant sheaf of rank 1 on $U$. We also give partial results on computation of cohomology groups on $U$ for a locally constant sheaf of general rank and on computation of $H^k(\C^n \setminus Z, \C)$ where $Z$ is a general algebraic set. Our algorithm is based on computations of Gröbner bases in the ring of differential operators with polynomial coefficients. | |
| dc.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/9801114 | |
| dc.identifier | http://arxiv.org/abs/math/9801114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76533 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F40;14Q99;55N30 | |
| dc.title | An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation | |
| dc.type | text |