Monodromy Eigenvalues Are Induced by Poles of Zeta Functions – the Irreducible Curve Case
نویسنده
چکیده
The ‘monodromy conjecture’ for a hypersurface singularity f predicts that a pole of its topological (or related) zeta function induces one of its monodromy eigenvalues. However, in general only a few eigenvalues are obtained this way. The second author proposed to consider zeta functions associated with the hypersurface and with a differential form and raised the following question. Can one find a list of differential forms ωi such that any pole of the zeta function of f and an ωi induces a monodromy eigenvalue of f , and such that all monodromy eigenvalues of f are obtained this way? Here we provide an affirmative answer for an arbitrary irreducible curve singularity f .
منابع مشابه
Monodromy Eigenvalues and Zeta Functions with Differential Forms
For a complex polynomial or analytic function f , there is a strong correspondence between poles of the so-called local zeta functions or complex powers ∫ |f |2sω, where the ω are C∞ differential forms with compact support, and eigenvalues of the local monodromy of f . In particular Barlet showed that each monodromy eigenvalue of f is of the form exp(2π −1s0), where s0 is such a pole. We prove ...
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