Curves contracted by the Gauss map

Abstract

Given a singular projective variety in some projective space, we characterize the smooth curves contracted by the Gauss map in terms of normal bundles. As a consequence, we show that if the variety is normal, then a contracted line always has local obstruction for the embedded deformation and each component of the Hilbert scheme where the line lies is non-reduced everywhere.

arXiv commentA section of examples and an appendix are added. Assumptions in Thm 1.2 are weaken