Rational curves on smooth cubic hypersurfaces over finite fields
Algebraic Geometry
2016-11-04 v2 Number Theory
Abstract
Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.
Cite
@article{arxiv.1502.05028,
title = {Rational curves on smooth cubic hypersurfaces over finite fields},
author = {Tim Browning and Pankaj Vishe},
journal= {arXiv preprint arXiv:1502.05028},
year = {2016}
}
Comments
12 pages; withdrawn since subsumed by the argument in arXiv:1611.00553