On the second gaussian map for curves on a K3 surface

Details On the second gaussian map for curves on a K3 surface On the second gaussian map for curves on a K3 surface

2009-05-14

arxiv.org/abs/0905.2330v3

Mathematics

Algebraic Geometry

final version, to appear in Nagoya Mathematical Journal

Scientific paper

By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first gaussian map is not surjective. In this paper we prove that if C is a general hyperplane section of high genus (greater than 280) of a general polarized K3 surface, then the second gaussian map of C is surjective. The resulting bound for the genus g of a general curve with surjective second gaussian map is decreased to g >152.

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