|Title||An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation|
|Author(s)|| Toshinori Oaku, Nobuki Takayama|
|Type||Article in Journal|
|Abstract||We 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.
|Copyright||Elsevier Science B.V.|
|Journal||Journal of Pure and Applied Algebra|