K3 Projective Models in Scrolls (Lecture Notes in Mathematics, 1842) 2004th Edition by Andreas L. Knutsen (PDF)

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.

User’s Reviews

Editorial Reviews: Review From the reviews:”The aim of this book is to give a description of projective models of K3 surfaces. It is clearly written and presents a complete exposition on the subject. The proofs use a variety of important techniques in projective geometry. … A graduate student interested in projective algebraic geometry could find this book quite useful and inspiring.” (Sandra Di Rocco, Mathematical Reviews, Issue 2005 g) From the Back Cover 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.

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