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Manin's conjecture for the chordal cubic fourfold

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arxiv 2504.16051 v1 pith:NUO2ZTCQ submitted 2025-04-22 math.NT math.AG

Ulrich Derenthal This is my paper · ORCID
classification math.NTmath.AG
keywords chordalcubicfourfoldconjecturemaninplaneprojectivecounting
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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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Cited by 1 Pith paper

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  1. Counting quadratic points on Fano varieties

    math.NT 2025-05 conditional novelty 7.0 of 10

    The count of quadratic point pairs on the non-split quadrics x^2 - d y^2 = z w matches the predicted c B log B, once a thin set of new flavour (contributing the same order) is removed.

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