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.
"Equinormalizability and topologically triviality of deformations of isolated curve singularities over smooth base spaces." Kodai Math. J. 38 (3) 642 - 657, October 2015. https://doi.org/10.2996/kmj/1446210599