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Article overview
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Low degree points on curves | | Geoffrey Smith
; Isabel Vogt
; | | Date: |
6 Jun 2019 | | 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 $P in C(ar{k})$ with $[k(P):k] leq e$.
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. | | Source: | arXiv, 1906.2328 | | Services: | Forum | Review | PDF | Favorites | |
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