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

Juliana Coelho

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arXiv · 2308.00098

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

Juliana Coelho

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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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Juliana Coelho. 2023-07-31. Gonality of curves whose normalizations are one or two copies of $\mathbb P^1$. https://arxiv.org/abs/2308.00098

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