The strong topological monodromy conjecture for Weyl hyperplane arrangements

Abstract

The Bernstein-Sato polynomial, or the b-function, is an important invariant of hypersurface singularities. The local topological zeta function is also an invariant of hypersurface singularities that has a combinatorial description in terms of a resolution of singularities. The Strong Topological Monodromy Conjecture of Denef and Loeser states that poles of the local topological zeta function are also roots of the b-function. We use a result of Opdam to produce a lower bound for the b-function of hyperplane arrangements of Weyl type. This bound proves the "n/d conjecture", by Budur, Mustaţǎ, and Teitler for this class of arrangements, which implies the Strong Monodromy Conjecture for this class of arrangements.