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Manin's conjecture for integral points on toric varieties

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arxiv 2312.13914 v2 pith:YML7RXZH submitted 2023-12-21 math.NT math.AG

classification math.NTmath.AG
keywords conjecturevarietiesmaninpointsboundedconstantfanogive
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We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded height on Fano varieties. We also give a prediction for the leading constant which is similar to Peyre's interpretation of the leading constant in Manin's conjecture. We give evidence for our conjecture by proving it for toric varieties. The proof is based on harmonic analysis on universal torsors.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Equidistribution and the torsor method

    math.NT 2026-07 accept novelty 7.0 of 10

    Rational points outside the lines on a smooth split quintic del Pezzo surface are equidistributed in the adelic space with respect to any anticanonical height, with limit measure the Tamagawa measure.

  2. Counting abelian number fields with restricted ramification type

    math.NT 2025-07 conditional novelty 7.0 of 10

    For finite abelian G, G-extensions of bounded height with restricted tame ramification type satisfy an explicit Malle-type asymptotic whose constant is governed by a partially unramified Brauer group.

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