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 / E. Colombo, P. Frediani. - In: NAGOYA MATHEMATICAL JOURNAL. - ISSN 0027-7630. - 199:(2010 Sep), pp. 123-136. [10.1215/00277630-2010-006]
On the second Gaussian map for curves on a K3 surface
E. Colombo
Primo
;
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 >152.
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