Gonality and Clifford index of curves on elliptic K3 surfaces with Picard number two

TL;DR

This paper calculates the Clifford index for all curves on a specific class of K3 surfaces with Picard number two, providing insights into their geometric properties.

Contribution

It introduces a method to compute the Clifford index for curves on elliptic K3 surfaces with Picard group U(m).

Findings

Clifford index values are explicitly determined for these curves.

The results reveal new relationships between surface geometry and curve invariants.

The work extends understanding of curve invariants on K3 surfaces.

Abstract

We compute the Clifford index of all curves on a K3 surface with Picard group isomorphic to U(m).