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1 November 2020 Density of rational points on a quadric bundle in P 3 × P 3
T. D. Browning, D. R. Heath-Brown
Duke Math. J. 169(16): 3099-3165 (1 November 2020). DOI: 10.1215/00127094-2020-0031

Abstract

We establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski-dense subset of the biprojective hypersurface x 1 y 1 2 + + x 4 y 4 2 = 0 in P 3 × P 3 . This confirms the modified Manin conjecture for this variety, in which the removal of a “thin” set of rational points is allowed.

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T. D. Browning. D. R. Heath-Brown. "Density of rational points on a quadric bundle in P 3 × P 3 ." Duke Math. J. 169 (16) 3099 - 3165, 1 November 2020. https://doi.org/10.1215/00127094-2020-0031

Information

Received: 29 May 2018; Revised: 9 March 2020; Published: 1 November 2020
First available in Project Euclid: 10 September 2020

MathSciNet: MR4167086
Digital Object Identifier: 10.1215/00127094-2020-0031

Subjects:
Primary: 11D45
Secondary: 11G50, 11P55, 14G05, 14G25

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 16 • 1 November 2020
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