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Rational points on del Pezzo surfaces of low degree

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arxiv 2401.04759 v1 pith:J5QW4XP5 submitted 2024-01-09 math.NT math.AG

Jakob Glas , Leonhard Hochfilzer This is my paper · ORCID
classification math.NTmath.AG
keywords characteristicpezzosurfacesdegreenumberpointsrationalanti-canonical
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We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results are conditional on a conjecture relating the rank of an elliptic curve to its conductor, while they are unconditional in positive characteristic. For quartic or quintic del Pezzo surfaces with a conic bundle structure, we establish even stronger estimates unconditionally as long as the characteristic is not two.

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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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