We study the second Gaussian map for a curve of genus g, in relation with the second fundamental form of the period map j : Mg ! Ag. We exhibit a class of infinitely many curves with surjective second Gaussian map. We compute its rank on the hyperelliptic and trigonal locus and show global generation of its image in H0(X, 4KX) for X not hyperelliptic nor trigonal.
Some results on the second Gaussian map for curves / E. Colombo, P. Frediani. - In: MICHIGAN MATHEMATICAL JOURNAL. - ISSN 0026-2285. - 58:3(2009), pp. 745-758.
Some results on the second Gaussian map for curves
E. Colombo;
2009
Abstract
We study the second Gaussian map for a curve of genus g, in relation with the second fundamental form of the period map j : Mg ! Ag. We exhibit a class of infinitely many curves with surjective second Gaussian map. We compute its rank on the hyperelliptic and trigonal locus and show global generation of its image in H0(X, 4KX) for X not hyperelliptic nor trigonal.
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