Rational curves on smooth cubic hypersurfaces over finite fields

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.

12 pages; withdrawn since subsumed by the argument in arXiv:1611.00553

References in corpus (2)

• Birch's theorem in function fields
• Rational points on cubic hypersurfaces over ${\mathbb{F}}_q(t)$

Cited by in corpus (1)

• Rational points on cubic hypersurfaces over ${\mathbb{F}}_q(t)$