On the surjectivity of the canonical Gaussian map for multiple coverings

Details On the surjectivity of the canonical Gaussian map for multiple coverings On the surjectivity of the canonical Gaussian map for multiple coverings

2004-03-22

arxiv.org/abs/math/0403354v1

Mathematics

Algebraic Geometry

Scientific paper

Here we investigate the canonical Gaussian map for higher multiple coverings of curves, the case of double coverings being completely understood thanks to previous work by Duflot. In particular, we prove that every smooth curve can be covered with degree not too high by a smooth curve having arbitrarily large genus and surjective canonical Gaussian map. As a consequence, we recover an asymptotic version of a recent result by Ciliberto and Lopez and we address the Arbarello subvariety in the moduli space of curves.

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