Cox rings of K3 surfaces with Picard number two

TL;DR

This paper investigates the structure of Cox rings for K3 surfaces with Picard number two, focusing on specific classical examples like quartic surfaces with a line and elliptic K3 surfaces.

Contribution

It provides new insights into the generators and relations of Cox rings for these specific K3 surface classes.

Findings

Identified generators of Cox rings for classical K3 surfaces.

Described relations among generators for these Cox rings.

Analyzed Cox rings of quartic and elliptic K3 surfaces.

Abstract

We study generators and relations of Cox rings of K3 surfaces of Picard number two. In particular we consider the Cox rings of classical examples of K3 surfaces, such as quartic surfaces containing a line and elliptic K3 surfaces.