K3 Projective Models in Scrolls

Trygve Johnsen, Andreas Leopold Knutsen3540215050, 9783540215059

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.

Table of contents :
1. Introduction….Pages 1-14
2. Surfaces in Scrolls….Pages 15-18
3. The Clifford index of smooth curves in |L| and the definition of the scrolls $mathcal{T}(c,D,{D_{lambda} })$ ….Pages 19-29
4. Two existence theorems….Pages 31-33
5. The singular locus of the surface S ’ and the scroll $mathcal{T}$ ….Pages 35-45
6. Postponed proofs….Pages 47-57
7. Projective models in smooth scrolls….Pages 59-61
8. Projective models in singular scrolls….Pages 63-98
9. More on projective models in smooth scrolls of K 3 surfaces of low Clifford-indices….Pages 99-120
10. BN general and Clifford general K 3 surfaces….Pages 121-128
11. Projective models of K 3 surfaces of low genus….Pages 129-154
12. Some applications and open questions….Pages 155-158
References….Pages 159-162