K3 projective models in scrolls

TL;DR

This paper investigates the projective models of certain polarized K3 surfaces, focusing on those contained in rational normal scrolls, and classifies models for genus up to 10.

Contribution

It provides a classification and detailed description of projective models of K3 surfaces of genus at most 10, especially those with non-general Clifford index.

Findings

Models are contained in rational normal scrolls.

Complete classification for genus up to 10.

Insights into the geometry of polarized K3 surfaces.

Abstract

We study the projective models of complex K3 surfaces polarized by a line bundle L such that all smooth curves in |L| have non-general Clifford index. Such models are in a natural way contained in rational normal scrolls. We use this study to classify and describe all projective models of K3 surfaces of genus at most 10.