Manin's conjecture for the chordal cubic fourfold
Number Theory
2025-04-23 v1 Algebraic Geometry
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.
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Cite
@article{arxiv.2504.16051,
title = {Manin's conjecture for the chordal cubic fourfold},
author = {Ulrich Derenthal},
journal= {arXiv preprint arXiv:2504.16051},
year = {2025}
}
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21 pages