Zeta functions and monodromy for surfaces that are general for a toric idealistic cluster
Algebraic Geometry
2008-02-21 v1
Abstract
In this article we consider surfaces that are general with respect to a 3- 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 eigenvalue. In a third part we prove the monodromy and the holomorphy conjecture for these surfaces.
Cite
@article{arxiv.0802.2730,
title = {Zeta functions and monodromy for surfaces that are general for a toric idealistic cluster},
author = {Ann Lemahieu and Willem Veys},
journal= {arXiv preprint arXiv:0802.2730},
year = {2008}
}