English

Separable rational connectedness and stability

Algebraic Geometry 2014-07-30 v3

Abstract

In this short note we prove that in many cases the failure of a variety to be separably rationally connected is caused by the instability of the tangent sheaf (if there are no other obvious reasons). A simple application of the results proves that a smooth Fano complete intersection is separably rationally connected if and only if it is separably uniruled. In particular, a general such Fano complete intersection is separably rationally connected.

Keywords

Cite

@article{arxiv.1312.4238,
  title  = {Separable rational connectedness and stability},
  author = {Zhiyu Tian},
  journal= {arXiv preprint arXiv:1312.4238},
  year   = {2014}
}

Comments

6 pages. Reference and acknowledgement added. Comments are welcome

R2 v1 2026-06-22T02:28:06.875Z