Some results on the second Gaussian map for curves

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We study the second Gaussian map for a curve X of genus g, in relation with
the second fundamental form of the period map. 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 for X
not hyperelliptic nor trigonal.

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