Polar loci of multivariable archimedean zeta functions

2025/04/14 by Nero Budur, Quan Shi, Budur, Nero +3 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2504.10051

openalex publication_date 2025/04/14 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We determine, up to exponentiating, the polar locus of the multivariable archimedean zeta function associated to a finite collection of polynomials F. The result is the monodromy support locus of F, a topological invariant. We give a relation between the multiplicities of the irreducible components of the monodromy support locus and the polar orders. These generalize results of Barlet for the case when F is a single polynomial. Our result determines the slopes of the polar locus of the zeta function of F, closing a circle of results of Loeser, Maisonobe, Sabbah. We apply our main result to elucidate the topological information contained by the oblique part of the zero locus of any ideal of Bernstein-Sato type.

Cited by

• On the Poles of Real Archimedean Zeta Functions
• On the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals

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