Zeta functions and monodromy for surfaces that are general for a toric idealistic cluster

2008/02/19 by Ann Lemahieu, Lemahieu, Ann, Willem Veys +1
Mathematics · #14B05 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0802.2730

openalex publication_date 2008/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Topological zeta functions of complex plane curve singularities
• Igusa's p-adic local zeta function and the Monodromy Conjecture for non-degenerated surface singularities
• The monodromy conjecture for a space monomial curve with a plane\n semigroup
• The monodromy conjecture for zeta functions associated to ideals in dimension two
• Introduction to the monodromy conjecture