Rational curves on cubic hypersurfaces over finite fields

2018/04/16 by Mânzăţeanu, Adelina
#11G35 (11P55 #11T55 #14G05) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1804.05643

Abstract

Given a smooth cubic hypersurface X over a finite field of characteristic greater than 3 and two generic points on X, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number of degree d rational curves on X passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough d.

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