Higher-dimensional analogues of K3 surfaces

Details Higher-dimensional analogues of K3 surfaces Higher-dimensional analogues of K3 surfaces

2010-05-18

arxiv.org/abs/1005.3131v1

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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