Second gonality of smooth aCM curves on quartic surfaces in ${\mathbb{P}}^3$

Abstract

For a smooth irreducible curve $C$, its second gonality $d_2$ is defined to be the minimum integer $d$ such that $C$ admits a linear series $g_d^2$. In this paper, we compute the second gonality of a smooth aCM curve $C$ lying on a smooth quartic surface in ${\mathbb{P}}^3$, whose Clifford index is computed by a net on $C$.

arXiv comment19 pages