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TitleCohomology, stratifications and parametric Gröbner bases in characteristic zero
Author(s) Uli Walther
TypeArticle in Journal
AbstractLet 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.
Length18
ISSN0747-7171
File
LanguageEnglish
JournalJournal of Symbolic Computation
Volume35
Number5
Pages527-542
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year2003
Translation No
Refereed No
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