Some Results on the Second Gaussian Map for Curves

@inproceedings{Colombo2008SomeRO,
title={Some Results on the Second Gaussian Map for Curves},
author={Elisabetta Colombo and Paola Frediani},
year={2008}
}

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 H(X, 4KX ) for X not hyperelliptic nor trigonal.