Fano threefolds and K3 surfaces

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)).

Plain TeX, 9 pages

Cited by in corpus (10)

• On the extendability of projective surfaces and a genus bound for Enriques-Fano threefolds
• Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds
• Maximal variation of curves on K3 surfaces
• Arithmetic occult period maps
• Disconnecting the moduli space of G_2-metrics via U(4)-coboundary defects
• Nu-invariants of extra-twisted connected sums
• Decomposition of Lagrangian classes on K3 surfaces
• Fano manifolds of degree ten and EPW sextics
• Fano-Mathieu correspondence
• The Chow rings of moduli spaces of elliptic surfaces over ${\mathbb{P}}^1$