1998/01/26 by Toshinori Ôaku, Toshinori Oaku, Oaku, Toshinori +2 · 1 citation
Computer Science · Mathematics · #14F40 #14Q99 #55N30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14F40 #msc:14Q99 #msc:55N30
paper · pdf · doi:10.48550/arxiv.math/9801114
38 pages
arxiv created 1998/01/26 · openalex publication_date 1998/01/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an algorithm to compute the following cohomology groups on U = \Cn ∖ V(f) for any non-zero polynomial f ∈ \Q[x1, ..., xn]; 1. Hk(U, \CU), \CU is the constant sheaf on U with stalk \C. 2. Hk(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 Hk(\Cn ∖ 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.