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Ciro Ciliberto, Università di Roma Tor Vergata

Gaussian maps for curves

In this talk I will recall the definition and properties of gaussian maps for curves. I will then concentrate on the second gaussian map, which is related to the second fundamental form of the moduli space of curves. I will finally talk about a recent result in collaboration with A. Calabri and R. Miranda, to the effect that the second gaussian map has maximal rank for a general curve of genus $g$.