Monodromy conjecture for nondegenerate surface singularities

Lemahieu, Ann; Van Proeyen, Lise

doi:10.1090/S0002-9947-2011-05301-8

Monodromy conjecture for nondegenerate surface singularities
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by Ann Lemahieu and Lise Van Proeyen PDF

Trans. Amer. Math. Soc. 363 (2011), 4801-4829 Request permission

Abstract:

We prove the monodromy conjecture for the topological zeta function for all nondegenerate surface singularities. Fundamental in our work is a detailed study of the formula for the zeta function of monodromy by Varchenko and the study of the candidate poles of the topological zeta function yielded by what we call ‘$B_1$-facets’. In particular, new cases among the nondegenerate surface singularities for which the monodromy conjecture is now proven are the nonisolated singularities, the singularities giving rise to a topological zeta function with multiple candidate poles and the ones for which the Newton polyhedron contains a $B_1$-facet.

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