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Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface

Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface J. Eur. Math. Soc. 4, 363–404 (2002) Digital Object Identifier (DOI) 10.1007/s100970200042 Claire Voisin Green’s generic syzygy conjecture for curves of even genus lying on a K3surface Received June 6, 2001 / final version received January 30, 2002 Published online July 9, 2002 –  c Springer-Verlag & EMS 2002 1. Introduction If C is a smooth projective curve of genus g and K is its canonical bundle, the theorem of Noether asserts that the multiplication map 0 0 0 ⊗2 µ : H (C, K ) ⊗ H (C, K ) → H C, K 0 C C is surjective when C is non hyperelliptic. The theorem of Petri concerns then the ideal I of C in its canonical embedding, assuming C is not hyperelliptic. It says that I is generated by its elements of degree 2if C is neither trigonal nor a plane quintic. In [7], M. Green introduced and studied the Koszul complexes p+1 p 0 0 q−1 0 0 q H ( X, L) ⊗ H ( X, L ) → H ( X, L) ⊗ H ( X, L ) p−1 0 0 q+1 → H ( X, L) ⊗ H ( X, L http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Green’s generic syzygy conjecture for curves of even genus lying on a K3 surface

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970200042
Publisher site
See Article on Publisher Site

Abstract

J. Eur. Math. Soc. 4, 363–404 (2002) Digital Object Identifier (DOI) 10.1007/s100970200042 Claire Voisin Green’s generic syzygy conjecture for curves of even genus lying on a K3surface Received June 6, 2001 / final version received January 30, 2002 Published online July 9, 2002 –  c Springer-Verlag & EMS 2002 1. Introduction If C is a smooth projective curve of genus g and K is its canonical bundle, the theorem of Noether asserts that the multiplication map 0 0 0 ⊗2 µ : H (C, K ) ⊗ H (C, K ) → H C, K 0 C C is surjective when C is non hyperelliptic. The theorem of Petri concerns then the ideal I of C in its canonical embedding, assuming C is not hyperelliptic. It says that I is generated by its elements of degree 2if C is neither trigonal nor a plane quintic. In [7], M. Green introduced and studied the Koszul complexes p+1 p 0 0 q−1 0 0 q H ( X, L) ⊗ H ( X, L ) → H ( X, L) ⊗ H ( X, L ) p−1 0 0 q+1 → H ( X, L) ⊗ H ( X, L

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Nov 1, 2002

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