Equinormalizable theory for plane curve singularities with embedded points and the theory of equisingularity

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

“…The author considered in [12] (2012) deformations of plane curve singularities with embedded components over smooth base spaces of dimension ≥ 1, and gave a similar δ-constant criterion for equinormalizability of these deformations, using special techniques (e.g. a corollary of Hilbert-Burch theorem), which are effective only for plane curve singularities.…”

“…The first purpose of this paper is to generalize the δ-constant criterion given in [3] and [12] to deformations of isolated (not necessarily reduced) curve singularities over normal or smooth base spaces of dimension ≥ 1. In Proposition 3.4 we show that equinormalizability of deformations of isolated curve singularities over normal base spaces implies the constancy of the δ number of fibers of these deformations.…”