Abstract
Abstract Making suitable generalizations of known results we prove some general facts about Gaussian maps. These facts 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 ≥ 7 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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