Detaching embedded points

Abstract

We show that if $D\subset {\mathbb{P}}^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\le 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus, show the smoothness of the Hilbert component whose general member is a plane curve union a point in ${\mathbb{P}}^3$, and construct a Hilbert component whose general member has an embedded point.

16 pages, amsart style. New examples added to show that hypotheses of main theorem are necessary, showing sharpness of result