Equisingular Deformations of Plane Curve and of Sandwiched Singularities

Original · EN

Let C be an isolated plane curve singularity, and (C,l) be a decorated curve. In this article we compare the equisingular deformations of C and the sandwiched singularity X(C,l). We will prove that for l ≫ 0 the functor of equisingular deformations of C and (C,l) are equivalent. From this we deduce a proof of a formula for the dimension of the equisingular stratum. Furthermore we will show how compute the equisingularity ideal of the curve singularity C, given the minimal (good) resolution of C.