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arXiv · 2604.24523

Denef-Loeser zeta functions of suspensions and Lê-Yomdin singularities

Enrique Artal Bartolo·Pedro D. González Pérez·Manuel González Villa·Edwin León Cardenal
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Abstract

The holomorphy conjecture for suspensions of plane curve singularities and the holomorphy and monodromy conjectures for Lê-Yomdin singularities of surfaces are proved. The first part of this paper provides formulæ for the motivic and topological zeta functions for a family of hypersurfaces, including the suspensions by an arbitrary number of points and which are more general than Thom-Sebastiani type. These formulae generalize and are inspired by the description of the topological and the 2-twisted topological zeta functions of suspensions by 2 points of hypersurfaces, due to the first named author, Cassou-Noguès, Luengo and Melle. The new general formulæ deal with arbitrary values of the twisting parameter. An interesting feature of these general formulæ is the appearance of values of the Jordan's totient function as coefficients of the topological and the twisted topological zeta functions of some auxiliary hypersurfaces of smaller dimension.

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Enrique Artal Bartolo, Pedro D. González Pérez, Manuel González Villa, Edwin León Cardenal. 2026-04-27. Denef-Loeser zeta functions of suspensions and Lê-Yomdin singularities. https://arxiv.org/abs/2604.24523

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