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

Juliana Coelho

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

Algebraic Geometry 2023-10-27 v2

Authors: Juliana Coelho

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.

Keywords

gonality curves normalization nodal curves binary curves genus

Cite

@article{arxiv.2308.00098,
  title  = {Gonality of curves whose normalizations are one or two copies of $\mathbb P^1$},
  author = {Juliana Coelho},
  journal= {arXiv preprint arXiv:2308.00098},
  year   = {2023}
}

Comments

12 pages, 2 figures. Comments welcome. arXiv admin note: text overlap with arXiv:2003.09331

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