Manin's conjecture for the chordal cubic fourfold

authored by

Ulrich Derenthal

Abstract

We prove the thin set version of Manin's conjecture for the chordal (or: determinantal) cubic fourfold, which is the secant variety of the Veronese surface. We reduce this counting problem to a result of Schmidt for quadratic points in the projective plane by showing that the chordal cubic fourfold is isomorphic to the symmetric square of the projective plane over the rational numbers.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Preprint

Publication date

22.04.2025

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2504.16051 (Access: Open)