K3 projective models in scrolls

2001/08/28 by Trygve Johnsen, Johnsen, Trygve, Andreas Leopold Knutsen +1
Mathematics · #14J28 (14H51) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0108183

This is a shorter version of (most of) SLN 1842

arxiv created 2005/04/12 · arxiv updated 2009/11/30

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.

Related

• P^r-scrolls arising from Brill-Noether theory and K3-surfaces
• Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5
• Triple solids and scrolls
• Higher rank Clifford indices of curves on a K3 surface
• Projective models for Hilbert squares of K3 surfaces