Mathematical Research Letters
Volume 24 (2017)
The strong topological monodromy conjecture for Weyl hyperplane arrangements
Pages: 947 – 954
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, Mustaţă, and Teitler for this class of arrangements, which implies the Strong Monodromy Conjecture for this class of arrangements.
Received 11 August 2015
Accepted 10 December 2015
Published 9 November 2017