Zeta Functions and Monodromy for Surfaces that are General for a Toric Idealistic Cluster

Ann Lemahieu (1) , Willem Veys (2)

1 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
2 Department of Mathematics

In this article, we consider surfaces that are general with respect to a three-dimensional toric idealistic cluster. In particular, this means that blowing up a toric constellation provides an embedded resolution of singularities for these surfaces. First we give a formula for the topological zeta function directly in terms of the cluster. Then we study the eigenvalues of monodromy. In particular, we derive a useful criterion to be an eigen-value. In a third part, we prove the monodromy and the holomorphy conjecture for these surfaces.

Domaines: Mathématiques [math]

Ann Lemahieu, Willem Veys. Zeta Functions and Monodromy for Surfaces that are General for a Toric Idealistic Cluster. International Mathematics Research Notices, 2009, 9 (1), pp.11-62. ⟨10.1093/imrn/rnn122⟩. ⟨hal-01279765⟩