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

Abstract

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