Density of rational points on some quadric bundle threefolds

Bonolis, Dante; Browning, Tim; Huang, Zhizhong

doi:10.1007/s00208-024-02854-4

Math. Ann.

2024

DOI: 10.1007/s00208-024-02854-4

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Density of rational points on some quadric bundle threefolds

Dante Bonolis,

Tim Browning,

Zhizhong Huang

Abstract: We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2).

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The Manin–Peyre conjecture for smooth spherical Fano threefolds

Blomer,

Brüdern,

Derenthal

et al. 2024

Sel. Math. New Ser.

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The Manin–Peyre conjecture is established for smooth spherical Fano threefolds of semisimple rank one and type N. Together with the previously solved case T and the toric cases, this covers all types of smooth spherical Fano threefolds. The case N features a number of structural novelties; most notably, one may lose regularity of the ambient toric variety, the height conditions may contain fractional exponents, and it may be necessary to exclude a thin subset with exceptionally many rational points from the count, as otherwise Manin’s conjecture in its original form would turn out to be incorrect.

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The Manin–Peyre conjecture for smooth spherical Fano threefolds

Blomer,

Brüdern,

Derenthal

et al. 2024

Sel. Math. New Ser.

View full text Add to dashboard Cite

show abstract

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Density of rational points on some quadric bundle threefolds

Abstract: We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2).

Cited by 1 publication

References 25 publications

The Manin–Peyre conjecture for smooth spherical Fano threefolds

The Manin–Peyre conjecture for smooth spherical Fano threefolds

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