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 Title Cohomology, stratifications and parametric Gröbner bases in characteristic zero Author(s) Uli Walther Type Article in Journal Abstract Let P_K(n,d) be the set of polynomials in n variables of degree at most d over the field K of characteristic zero. We show that there is a number c_{n,d} such that if f \in P_K(n,d) then the algebraic de Rham cohomology group H^i_{dR} (K^n \ Var(f)) has rank at most c_{n,d}. We also show the existence of a bound c_{n,d,l} for the ranks of de Rham cohomology groups of complements of varieties in n-space defined by the vanishing of l polynomials in P_k(n,d). In fact, if \beta_i : P_K(n,d)^l \rightarrow N is the i-th Betti number of the complement of the corresponding variety, we establish the existence of a Q-algebraic stratification on P_K(n,d)^l such that \beta_i is constant on each stratum. The stratifications arise naturally from parametric Gröbner basis computations; we prove for parameter-insensitive weight orders in Weyl algebras the existence of specializing Gröbner bases. Length 18 ISSN 0747-7171 File Language English Journal Journal of Symbolic Computation Volume 35 Number 5 Pages 527-542 Publisher Academic Press, Inc. Address Duluth, MN, USA Year 2003 Translation No Refereed No
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