1. Low Degree Points on Curves.
- Author
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Smith, Geoffrey and Vogt, Isabel
- Subjects
- *
ARITHMETIC , *CURVES - 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 that there are infinitely many points |$P \in C(\bar{k})$| with |$[k(P):k] \leqslant e$|. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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