Fano threefolds and K3 surfaces

Arnaud Beauville

Fano threefolds and K3 surfaces

Algebraic Geometry 2007-05-23 v1

Authors: Arnaud Beauville

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

Keywords

fano varieties algebraic surfaces

Cite

@article{arxiv.math/0211313,
  title  = {Fano threefolds and K3 surfaces},
  author = {Arnaud Beauville},
  journal= {arXiv preprint arXiv:math/0211313},
  year   = {2007}
}

Comments

Plain TeX, 9 pages

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