Higher-dimensional analogues of K3 surfaces
arXiv:1005.3131
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).
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