Low Degree Points on Curves

DOI10.1093/IMRN/RNAA137zbMATH Open1490.14052arXiv1906.02328OpenAlexW3038669928MaRDI QIDQ5022120

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Publication date: 18 January 2022

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: In this paper we investigate an arithmetic analogue of the gonality of a smooth projective curve $C$ over a number field $k$: the minimal $e$ such there are infinitely many points $$ with $[k(P):k]leqe$. Developing techniques that make use of an auxiliary smooth surface containing the curve, we show that this invariant can take any value subject to constraints imposed by the gonality. Building on work of Debarre--Klassen, we show that this invariant is equal to the gonality for all sufficiently ample curves on a surface $S$ with trivial irregularity.

Full work available at URL: https://arxiv.org/abs/1906.02328

Mathematics Subject Classification ID

Rational points (14G05) Special divisors on curves (gonality, Brill-Noether theory) (14H51)

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