Fano threefolds and K3 surfaces

2002/11/20 by Arnaud Beauville, Beauville, Arnaud · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0211313

Plain TeX, 9 pages

arxiv created 2002/11/20 · arxiv updated 2009/11/30

Abstract

We discuss in this note which K3 surfaces appear as anticanonical divisors in a Fano threefold. We prove in particular that a general K3 surface with given Picard lattice P and polarization class h in P is an anticanonical divisor in a Fano threefold if and only if (P,h) is isomorphic to (Pic(V), c₁(V)) for some Fano threefold V, where Pic(V) is equipped with the intersection product (L,M) --> (L.M.c₁(V)).

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