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arXiv · 0910.2179

The monodromy conjecture for zeta functions associated to ideals in dimension two

Lise Van Proeyen·Willem Veys
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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.

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BibTeXRIS

Lise Van Proeyen, Willem Veys. 2009-10-12. The monodromy conjecture for zeta functions associated to ideals in dimension two. https://arxiv.org/abs/0910.2179

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