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- W2070278770 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 ∈ P K ( n , d ) then the algebraic de Rham cohomology group H dR i ( 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 β i :P K (n,d) l → 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 β 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." @default.
- W2070278770 created "2016-06-24" @default.
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- W2070278770 date "2003-05-01" @default.
- W2070278770 modified "2023-09-29" @default.
- W2070278770 title "Cohomology, stratifications and parametric Gröbner bases in characteristic zero" @default.
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- W2070278770 doi "https://doi.org/10.1016/s0747-7171(03)00019-1" @default.
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