On the second gaussian map for curves on a K3 surface

2009/05/14 by Elisabetta Colombo, Paola Frediani, Colombo, Elisabetta +1
Mathematics · #14H10 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:14J28

paper · pdf · doi:10.48550/arxiv.0905.2330

final version, to appear in Nagoya Mathematical Journal

arxiv created 2010/03/04 · arxiv updated 2010/03/05

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 (greater than 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.

Related

• Higher Gaussian Maps on K3 surfaces
• On hyperplane sections of K3 surfaces
• Surjectivity of Gaussian maps for curves on Enriques surfaces
• The rank of the 2nd Gaussian map for general curves
• Some results on the second Gaussian map for curves