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

For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs, we consider general types of multivariate Bernstein–Sato ideals associated to arbitrary factorizations our germ. We show that these are principal, the zero loci different related by a diagonal property. If, additionally, divisor is hyperplane arrangement, obtain nice estimates for locus its ideal attached factorization into linear forms reduced. As an application, independently verify improve upon estimate Maisonobe regarding standard reduced, generic arrangements: compute forms, other factorizations.