The motivic Igusa zeta function of a space monomial curve with a plane semigroup-Reference-Cited by-同舟云学术

The motivic Igusa zeta function of a space monomial curve with a plane semigroup

Published:2021-07-10 Issue:0 Volume:0 Page:
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Mourtada Hussein¹,Veys Willem²,Vos Lena²

Affiliation:

1. Université de Paris, Sorbonne Université, CNRS , Institut de Mathématiques de Jussieu-Paris Rive Gauche , 75013 , Paris , France

2. KU Leuven, Departement Wiskunde , Celestijnenlaan 200B, bus 2400, 3001 , Leuven , Belgium

Abstract

Abstract In this article, we compute the motivic Igusa zeta function of a space monomial curve that appears as the special fiber of an equisingular family whose generic fiber is a complex plane branch. To this end, we determine the irreducible components of the jet schemes of such a space monomial curve. This approach does not only yield a closed formula for the motivic zeta function, but also allows to determine its poles. We show that, while the family of the jet schemes of the fibers is not flat, the number of poles of the motivic zeta function associated with the space monomial curve is equal to the number of poles of the motivic zeta function associated with a generic curve in the family.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2021-0009/pdf

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