Fano threefolds and K3 surfaces
By A. Beauville. 2002
70 citations recorded by the source corpus.
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)).
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e7ba4e14dfc2432d2fbc386ef83a48063ad003fb
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In Geometry and Topology
- Johannes Nordstrom
- M. Haskins
- T. Pacini
- Alessio Corti
- D. Huybrechts
- D. Joyce
- E. Markman
- Thomas Walpuski
Citations in the corpus
- Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds (2012, background): “Remark H2(Y, TY ) does not always vanish for a weak Fano Y (see [88, Example 2.7]) and therefore Beauville’s proof of smoothness of FN,A does not work in the general weak Fano setting.”
- Lectures on K3 Surfaces (2016, background): “1, and the papers by Dolgachev [148] and Beauville [47].”