Some results on Bernstein-Sato polynomials for parametric analytic functions. (English) Zbl 1109.32023

Bahloul, Rouchdi

Proc. Japan Acad., Ser. A 82, No. 3, 40-45 (2006).

Summary: This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters [see also R. Bahloul, Compos. Math. 141, No. 1, 175–191 (2005; Zbl 1099.32005)]. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) Bernstein-Sato polynomial.

MSC:

32S10	Invariants of analytic local rings
32S40	Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
16S32	Rings of differential operators (associative algebraic aspects)
13P99	Computational aspects and applications of commutative rings

Keywords:

Bernstein-Sato polynomial; deformation of singularities; generic standard bases

Citations:

Zbl 1099.32005

References:

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