K3 Projective Models in Scrolls

1. Auflage 2004
ISBN: 978-3-540-21505-9
Verlag: Springer

Buch, Englisch, Band 1842, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

The exposition studies projective models of 3 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 3 surfaces in projective spaces of low dimension, and leads to a classification of 3 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 3 surfaces and incorporating much of the Brill-Noether theory of curves and theory of syzygies developed in the mean time.

Zielgruppe

Research

Autoren/Hrsg.

Knutsen, Andreas L.

Johnsen, Trygve

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.