Higher-dimensional analogues of K3 surfaces

Abstract

In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product) is isomorphic to that of the Hilbert square of a K3 enjoy many of the beautiful properties of K3 surfaces, in particular they should form a single deformations class.

The paper originated from a talk given at MSRI during the special program in Algebraic Geometry (2009).

References in corpus (4)

• Hyper-Kähler fourfolds and Grassmann geometry
• Quelques remarques sur la décomposition de Zariski divisorielle sur les variétés dont la première classe de Chern est nulle
• La singularité de O'Grady
• Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces