An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation

dc.creatorOaku, Toshinori
dc.creatorTakayama, Nobuki
dc.date1998-01-26
dc.date.accessioned2026-07-07T05:23:40Z
dc.date.available2026-07-07T05:23:40Z
dc.descriptionWe 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.description38 pages
dc.identifierhttps://arxiv.org/abs/math/9801114
dc.identifierhttp://arxiv.org/abs/math/9801114
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76533
dc.subjectAlgebraic Geometry
dc.subject14F40;14Q99;55N30
dc.titleAn algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation
dc.typetext

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