Free curves in Fano hypersurfaces must have high degree
Algebraic Geometry
2026-03-10 v2
Abstract
The purpose of this note is to show that the minimal for which every smooth Fano hypersurface of dimension contains a free rational curve of degree at most cannot be bounded by a linear function in when the base field has positive characteristic. This is done by providing a super-linear bound on the minimal possible degree of a free curve in certain Fermat hypersurfaces.
Keywords
Cite
@article{arxiv.2404.17341,
title = {Free curves in Fano hypersurfaces must have high degree},
author = {Raymond Cheng},
journal= {arXiv preprint arXiv:2404.17341},
year = {2026}
}
Comments
5 pages, accepted version, comments always welcome!