スクロール内のＫ３射影モデル K3 Projective Models in Scrolls (Lecture Notes in Mathematics Vol.1842) （2004. VIII, 164 p.）

Johnsen, T./ Knutsen, A. L.

SPRINGER, BERLIN（2004発売）

SPRINGER, BERLIN（2004発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 164 p.
• 商品コード 9783540215059

Full Description

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.

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.