English

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.

Keywords

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12 pages; withdrawn since subsumed by the argument in arXiv:1611.00553

R2 v1 2026-06-22T08:31:46.303Z