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

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

1998-01-26

arxiv.org/abs/math/9801114v1

Mathematics

Algebraic Geometry

38 pages

Scientific paper

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 Gr\"obner bases in the ring of differential operators with polynomial coefficients.

Affiliated with

Also associated with

No associations

Rating

An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375571