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 .
On the second Gaussian map for curves on a K3 surface / E. Colombo, P. Frediani. - In: NAGOYA MATHEMATICAL JOURNAL. - ISSN 0027-7630. - 199(2010 Sep), pp. 123-136.
On the second Gaussian map for curves on a K3 surface
E. Colombo;
2010
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 .
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