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 (> 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.

On the second Gaussian map for curves on a K3 surface

FREDIANI, PAOLA
2010-01-01

Abstract

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 (> 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/204461
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