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On the second Gaussian map for curves on a K3 surface

Published online by Cambridge University Press:  11 January 2016

Elisabetta Colombo  and
Paola Frediani
Elisabetta Colombo
Affiliation:
Dipartimento di Matematica, Università di Milano, I-20133, Milano, Italy, elisabetta.colombo@unimi.it
Paola Frediani
Affiliation:
Dipartimento di Matematica, Università di Milano, I-20133, Milano, Italy, elisabetta.colombo@unimi.it
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Abstract

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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.

Keywords

14H1014J28
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 199 , September 2010 , pp. 123 - 136
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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