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Green’s conjecture for curves on arbitrary K3 surfaces

Part of: Cycles and subschemes Commutative algebra: Homological methods

Published online by Cambridge University Press:  15 February 2011

Marian Aprodu  and
Gavril Farkas
Marian Aprodu
Affiliation:
Institute of Mathematics ‘Simion Stoilow’ of the Romanian Academy, RO-014700 Bucharest, Romania (email: [email protected]) Şcoala Normală Superioară Bucureşti, Calea Griviţei 21, Sector 1, RO-010702 Bucharest, Romania
Gavril Farkas
Affiliation:
Humboldt-Universität zu Berlin, Institut Für Mathematik, 10099 Berlin, Germany (email: [email protected])
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Abstract

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Green’s conjecture predicts than one can read off special linear series on an algebraic curve, by looking at the syzygies of its canonical embedding. We extend Voisin’s results on syzygies of K3 sections, to the case of K3 surfaces with arbitrary Picard lattice. This, coupled with results of Voisin and Hirschowitz–Ramanan, provides a complete solution to Green’s conjecture for smooth curves on arbitrary K3 surfaces.

Keywords

syzygycanonical curveBrill–Noether theory

MSC classification

Secondary: 13D02: Syzygies, resolutions, complexes 14C20: Divisors, linear systems, invertible sheaves
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 3 , May 2011 , pp. 839 - 851
Copyright
Copyright © Foundation Compositio Mathematica 2011

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