Surjectivity of Gaussian maps for curves on Enriques surfaces

2006/10/05 by Andreas Leopold Knutsen, A. L. Knutsen, Angelo Felice Lopez +3
Computer Science · Engineering · Mathematics · #14H51 #14H99 #14J28 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H51 #msc:14H99 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0610173

latex, 28 pages. To appear on Adv. Geom

arxiv created 2006/10/05 · openalex publication_date 2006/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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