The Green Conjecture for Exceptional Curves on a K3 Surface

Details The Green Conjecture for Exceptional Curves on a K3 Surface The Green Conjecture for Exceptional Curves on a K3 Surface

2006-09-04

arxiv.org/abs/math/0609107v1

Mathematics

Algebraic Geometry

Scientific paper

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 at least three. We obtain our result by adopting an infinitesimal
approach due to Pareschi, and using a degenerate version of a theorem due to
Hirschowitz-Ramanan-Voisin.

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