Author	Johnsen, Trygve. author
Title	K3 Projective Models in Scrolls [electronic resource] / by Trygve Johnsen, Andreas Leopold Knutsen
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2004
Connect to	http://dx.doi.org/10.1007/b97183
Descript	VIII, 172 p. online resource

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 to a classification of K3 surfaces in projective spaces of dimension at most 10. The authors bring further the ideas in Saint-Donat's classical article from 1974, lifting results from canonical curves to K3 surfaces and incorporating much of the Brill-Noether theory of curves and theory of syzygies developed in the mean time

Introduction -- Surfaces in scrolls -- The Clifford index of smooth curves in | and the definition of the scrolls T(c, D, {D_{\lamda}}) -- Two existence theorems -- The singular locus of the surface Sยด 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

1. Mathematics
2. Algebraic geometry
3. Mathematics
4. Algebraic Geometry