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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.
List of 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.
Summary
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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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)
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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)
