Equinormalizability and topologically triviality of deformations of isolated curve singularities over smooth base spaces

TL;DR

This paper establishes a $elta$-constant criterion for equinormalizability of deformations of isolated curve singularities over smooth bases and links topological triviality to weak simultaneous resolutions in one-parameter families.

Contribution

It introduces a new $elta$-constant criterion for equinormalizability and connects topological triviality with weak simultaneous resolutions for certain curve singularity deformations.

Findings

elta-constant criterion for equinormalizability

Topological triviality equivalent to weak simultaneous resolutions

Applicable to non-reduced isolated curve singularities

Abstract

We give a $\delta$-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension $\geq 1$. For one-parametric families of isolated curve singularities, we show that their topologically triviality is equivalent to the admission of weak simultaneous resolutions.