Curves contracted by the Gauss map
Algebraic Geometry
2022-06-14 v2
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.
Keywords
Cite
@article{arxiv.2103.11159,
title = {Curves contracted by the Gauss map},
author = {Lei Song},
journal= {arXiv preprint arXiv:2103.11159},
year = {2022}
}
Comments
A section of examples and an appendix are added. Assumptions in Thm 1.2 are weaken