Cuspidal Multiple Structures on Smooth Algebraic Varieties as Support

Abstract

We construct lci nilpotent scheme structures $Y\subset P$ on a smooth variety $X$ embedded in a smooth variety $P$, which are, locally, (i.e. in ${\hat{\mathcal{O}}}_{p,P}$ ) given by ideals of the form $(y^2+x^n,xy,z_1,...,z_r)$, $(y^3+x^n,xy,z_1,...z_r)$