The monodromy conjecture for zeta functions associated to ideals in dimension two
Algebraic Geometry
2009-10-13 v1 Geometric Topology
Abstract
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot; however, in full generality it is proven only for zeta functions associated to a polynomial in two variables. In this article we consider zeta functions associated to an ideal. First we work in arbitrary dimension and obtain a formula (like the one of A'Campo) to compute the 'Verdier monodromy' eigenvalues associated to an ideal. Afterwards we prove a generalized monodromy conjecture for arbitrary ideals in two variables.
Cite
@article{arxiv.0910.2179,
title = {The monodromy conjecture for zeta functions associated to ideals in dimension two},
author = {Lise Van Proeyen and Willem Veys},
journal= {arXiv preprint arXiv:0910.2179},
year = {2009}
}
Comments
16 pages, to appear in Ann. Inst. Fourier