Nagoya Mathematical Journal

On the second Gaussian map for curves on a K3 surface

Elisabetta Colombo and Paola Frediani

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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.

Article information

Nagoya Math. J., Volume 199 (2010), 123-136.

First available in Project Euclid: 14 September 2010

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Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic) 14J28: $K3$ surfaces and Enriques surfaces


Colombo, Elisabetta; Frediani, Paola. On the second Gaussian map for curves on a K3 surface. Nagoya Math. J. 199 (2010), 123--136. doi:10.1215/00277630-2010-006.

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