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

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.

Categories: math.AG