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

TL;DR

This paper computes the second gonality of smooth aCM curves on quartic surfaces in P^3, focusing on cases where the Clifford index is determined by a net on the curve.

Contribution

It provides a new explicit computation of the second gonality for a class of curves on quartic surfaces, expanding understanding of their linear series.

Findings

Determined the second gonality for smooth aCM curves on quartic surfaces.

Connected the second gonality to the Clifford index computed by a net on the curve.

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 $C$.