A Note on Bernstein-Sato Varieties for Tame Divisors and Arrangements

Autor:	Bath, Daniel
Rok vydání:	2020
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Mathematics - Complex Variables
Druh dokumentu:	Working Paper
Popis:	For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs we consider general types of multivariate Bernstein-Sato ideals associated to arbitrary factorizations of our germ. We show the zero loci of these ideals are purely codimension one and the zero loci associated to different factorizations are related by a diagonal property. If, additionally, the divisor is a hyperplane arrangement, we show the Bernstein-Sato ideals attached to a factorization into linear forms are principal. As an application, we independently verify and improve an estimate of Maisonobe's regarding standard Bernstein-Sato ideals for reduced, generic arrangements: we compute the Bernstein-Sato ideal for a factorization into linear forms and we compute its zero locus for other factorizations. Comment: Reorganized due to new content: Theorem 1.2 (n+1-pure & relative holonomic implies that the Bernstein--Sato-ideal is principal); the Appendix (behavior of logarithmic forms for non-reduced divisors); other quality of life improvements. Final version to appear in Michigan Mathematical Journal
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.07447 Zobrazit plný text záznamu View this record from Arxiv