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Some remarks on morphisms between Fano threefolds

2004/05/11 by Ekaterina Amerik, Amerik, Ekaterina
Mathematics · #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/0405187

14 pages, LaTeX. A lemma added in Section 2

arxiv created 2004/05/21 · arxiv updated 2009/12/01

Abstract

Let X, Y be Fano threefolds of Picard number one and such that the ample generators of Picard groups are very ample. Let X be of index one and Y be of index two. It is shown that the only morphisms from X to Y are double coverings. In fact nearly the whole paper is the analysis of the case where Y is the linear section of the Grassmannian G(1,4), since the other cases were more or less solved in another article. This remaining case is treated with the help of Debarre's connectedness theorem for inverse images of Schubert cycles.

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