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TitleAn algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation
Author(s) Toshinori Oaku, Nobuki Takayama
TypeArticle in Journal
AbstractWe give an algorithm to compute the following cohomology groups on U=C^n-45 degree ruleV(f) for any non-zero polynomial fset membership, variantQ[x1, ... ,xn]:
1. H^k(U,CU), CU is the constant sheaf on U with stalk C.
2. Image 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-45 degree rule 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.
Length33
CopyrightElsevier Science B.V.
File
URL dx.doi.org/10.1016/S0022-4049(99)00012-2
LanguageEnglish
JournalJournal of Pure and Applied Algebra
Volume139
Number1-3
Pages201-233
Year1999
MonthJune
Translation No
Refereed No
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