Details:
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 nspace 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 ith Betti number of the complement of the corresponding variety, we establish the existence of a Qalgebraic 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 parameterinsensitive weight orders in Weyl algebras the existence of specializing Gröbner bases.  Length  18  ISSN  07477171 
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 Language  English  Journal  Journal of Symbolic Computation  Volume  35  Number  5  Pages  527542  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  2003  Translation 
No  Refereed 
No 
