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Gonality of curves whose normalizations are one or two copies of $\mathbb P^1$

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arxiv 2308.00098 v2 pith:HMJNRWER submitted 2023-07-31 math.AG

Juliana Coelho This is my paper · ORCID
classification math.AG
keywords casemathbbcopiescurvecurvesgonalitywhosebinary
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abstract

We study the gonality of curves $C$ over $\mathbb C$ whose normalization is composed of one or two copies of $\mathbb P^1$. In the first case, $C$ is a nodal curve with $g(C)$ nodes, and in the second case $C$ is a so-called binary curve. In any case we show that the usual bound $\mathrm{gon}(C)\leq\lfloor\frac{g(C)+3}{2}\rfloor$ holds if $g(C)\geq 2$, with equality holding generically.

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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. Semistable Reduction of Plane Quartics

    math.AG 2025-11 conditional novelty 7.0 of 10

    A plane quartic admits a GIT-stable plane model exactly when its stable reduction is non-hyperelliptic, and then the stable model is the unique minimal semistable model arising by resolving the cusps of the GIT model.

  2. Semistable reduction of smooth quartics

    math.AG 2026-06 conditional novelty 4.0 of 10

    For smooth plane quartics, non-hyperelliptic stable reduction is equivalent to the existence of a unique GIT-stable plane model, and the stable model is obtained by cusp resolution.

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