Work

Rational Curves on Cubic Hypersurfaces Over Finite Fields

Year: 2021

Type: article

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 $d$.

Source: Mathematika

DOI: 10.1112/mtk.12073

Author: Adelina Mânzăţeanu

Institution: Leiden University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,000

Funder: Engineering and Physical Sciences Research Council