K3 Projective Models in Scrolls

• Main Authors: Knutsen, Andreas L. (Author, http://id.loc.gov/vocabulary/relators/aut), Johnsen, Trygve (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Edition: 1st ed. 2004.
• Series: Lecture Notes in Mathematics, 1842
• Subjects: Algebraic geometry.; Algebraic Geometry.

The exposition studies projective models of K3 surfaces whose hyperplane sections are non-Clifford general curves. These models are contained in rational normal scrolls. The exposition supplements standard descriptions of models of general K3 surfaces in projective spaces of low dimension, and leads...

Table of Contents:

• Introduction
• Surfaces in scrolls
• The Clifford index of smooth curves in |L| and the definition of the scrolls T(c, D, {D_{\lamda}})
• Two existence theorems
• The singular locus of the surface S´ and the scroll T
• Postponed proofs
• Projective models in smooth scrolls
• Projective models in singular scrolls
• More on projective models in smooth scrolls of K3 surfaces of low Clifford-indices
• BN general and Clifford general K3 surfaces
• Projective models of K3 surfaces of low genus
• Some applications and open questions
• References
• Index.