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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn043, 25 pages, doi:10.1093/imrn/rnn043 published on May 6, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

The Green Conjecture for Exceptional Curves on a K3 Surface

Marian Aprodu1,2 and Gianluca Pacienza3

1 Institute of Mathematics "Simion Stoilow" of the Romanian Academy P.O. Box 1-764, 014700 Bucharest, Romania
2 Sçoala Normala Superioara Bucuresti, Calea Grivitei 21, Sector 1, 010702 Bucharest, Romania
3 Institut de Recherches Mathématiques Avancées Université Louis Pasteur et CNRS 7 rue René Descartes, 67084 Strasbourg Cedex, France

Correspondence: Correspondence to be sent to: pacienza{at}math.u-strasbg.fr

We use the Brill–Noether theory to prove the Green conjecture for exceptional curves on K3 surfaces. Such curves count among the few ones having Clifford dimension >=3. We obtain our result by adopting an infinitesimal approach due to Pareschi, and using the degenerate version of the Hirschowitz–Ramanan–Voisin theorem obtained in the paper [4].


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