Surjectivity of Gaussian maps for curves on Enriques surfaces

Details Surjectivity of Gaussian maps for curves on Enriques surfaces Surjectivity of Gaussian maps for curves on Enriques surfaces

2006-10-05

arxiv.org/abs/math/0610173v1

Mathematics

Algebraic Geometry

latex, 28 pages. To appear on Adv. Geom

Scientific paper

Making suitable generalizations of known results we prove some general facts about Gaussian maps. The above are then used, in the second part of the article, to give a set of conditions that insure the surjectivity of Gaussian maps for curves on Enriques surfaces. To do this we also solve a problem of independent interest: a tetragonal curve of genus g > 6 lying on an Enriques surface and general in its linear system, cannot be, in its canonical embedding, a quadric section of a surface of degree g - 1 in P^{g - 1}.

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