Brill-Noether general curves on Knutsen K3 surfaces

TL;DR

This paper classifies certain K3 surfaces with irreducible hyperplane sections and demonstrates that their general hyperplane sections are Brill-Noether general curves, expanding understanding of their geometric properties.

Contribution

It provides a classification of Knutsen K3 surfaces with irreducible hyperplane sections and shows these surfaces have general hyperplane sections that are Brill-Noether general curves.

Findings

Classified Knutsen K3 surfaces with irreducible hyperplane sections

Established existence of infinite families with Brill-Noether general hyperplane sections

Connected surface classification with properties of hyperplane sections

Abstract

This article classifies Knutsen K3 surfaces all of whose hyperplane sections are irreducible and reduced. As an application, this gives infinite families of K3 surfaces of Picard number two whose general hyperplane sections are Brill-Noether general curves.