Rational curves on smooth cubic hypersurfaces over finite fields

2015/02/17 by Browning, Tim, Vishe, Pankaj
#11P55 #14G05 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1502.05028

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.

Related

• Rational curves on cubic hypersurfaces over finite fields
• Looking for rational curves on cubic hypersurfaces
• Rational linear subspaces of hypersurfaces over finite fields
• Rational points on even dimensional Fermat cubics
• Rational lines on cubic hypersurfaces II