Work

Birational zeta functions

Year: 2025

Type: preprint

Abstract: We define a birational analog of the motivic zeta function of a reduced polynomial in terms of minimal models. It admits an intrinsic meaning in terms of contact loci of arcs, an analog of a result of Denef and Loeser in the motivic case. We show that for local plane curve singularities the poles of the birational zeta function essentially coincide with the poles of the motivic zeta function.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2509.03352

Authors: Biesbrouck, Tom, Budur, Nero, Nicaise, Johannes, Veys, Willem

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416717320

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