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On the second Gaussian map for curves on a K3 surface
Published online by Cambridge University Press: 11 January 2016
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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- Copyright © Editorial Board of Nagoya Mathematical Journal 2010
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