On delta for parameterized curve singularities

We consider families of parameterizations of reduced curve singularities over a Noetherian base scheme and prove that the delta invariant is semicontinuous. In our setting, each curve singularity in the family is the image of a parameterization and not the fiber of a morphism. The problem came up in...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2023-02, Vol.615, p.151-169
Main Authors: Greuel, Gert-Martin, Pfister, Gerhard
Format: Article
Language:English
Subjects:
Completed tensor product
Curve singularity
Delta invariant
Determinacy
Parameterization
Semicontinuity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider families of parameterizations of reduced curve singularities over a Noetherian base scheme and prove that the delta invariant is semicontinuous. In our setting, each curve singularity in the family is the image of a parameterization and not the fiber of a morphism. The problem came up in connection with the right-left classification of parameterizations of curve singularities defined over a field of positive characteristic. We prove a bound for right-left determinacy of a parameterization in terms of delta, and the semicontinuity theorem provides a simultaneous bound for the determinacy in a family. The fact that the base space can be an arbitrary Noetherian scheme causes some difficulties but is (not only) of interest for computational purposes.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.10.021