On the Normal Sheaf of Gorenstein Curves

Abstract

We show that any tetragonal Gorenstein integral curve is a complete intersection in its respective $3$-fold rational normal scroll S, implying that the normal sheaf on $C$ embedded in S, and in ${\mathbb{P}}^{g-1}$ as well, is unstable for $g\ge 5$, provided that $S$ is smooth. We also compute the degree of the normal sheaf of any singular reduced curve in terms of the Tjurina and Deligne numbers, providing a semicontinuity of the degree of the normal sheaf over suitable deformations, revisiting classical results of the local theory of analytic germs.

References in corpus (1)

• The normal bundle of canonical genus 8 curves