English

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

R2 v1 2026-06-24T00:22:45.309Z