Fano threefolds and K3 surfaces

Details Fano threefolds and K3 surfaces Fano threefolds and K3 surfaces

2002-11-20

arxiv.org/abs/math/0211313v1

Mathematics

Algebraic Geometry

Plain TeX, 9 pages

Scientific paper

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), c_1(V)) for some Fano threefold V, where Pic(V) is equipped with the intersection product (L,M) --> (L.M.c_1(V)).

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