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.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris 1842 3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo Trygve Johnsen Andreas Leopold Knutsen K3 Projective Models in Scrolls 13 Authors Trygve Johnsen Department of Mathematics University of Bergen Johs. Bruns gt. 12 5008 Bergen, Norway e-mail:
[email protected] Andreas Leopold Knutsen Department of Mathematics University of Oslo Box 1053, Blindern 0316 Oslo, Norway e-mail:
[email protected] Library of Congress Control Number: 2004103750 Mathematics Subject Classification (2000): 14J28, 14H51 ISSN 0075-8434 ISBN 3-540-21505-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reprodu