Cohomology, stratifications and parametric Gröbner bases in characteristic zero
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- 作者：Walther ; Uli
- 关键词：Parametric Grö ; bner bases ; Stratifications ; Cohomology
- 刊名：Journal of Symbolic Computation
- 出版年：2003
- 出版时间：May, 2003
- 年：2003
- 卷：35
- 期：5
- 页码：527-542
- 全文大小：193 K
文摘
Let PK(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 cn,d such that if f
PK(n,d) then the algebraic de Rham cohomology group HdRi(Kn
Var(f)) has rank at most cn,d. We also show the existence of a bound cn,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 PK(n,d). In fact, if βi:PK(n,d)l→N is the ith Betti number of the complement of the corresponding variety, we establish the existence of a Q-algebraic stratification on PK(n,d)l such that βi is constant on each stratum.
PK(n,d) then the algebraic de Rham cohomology group HdRi(KnVar(f)) has rank at most cn,d. We also show the existence of a bound cn,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 PK(n,d). In fact, if βi:PK(n,d)l→N is the ith Betti number of the complement of the corresponding variety, we establish the existence of a Q-algebraic stratification on PK(n,d)l such that βi is constant on each stratum.