Higher-dimensional analogues of K3 surfaces
Algebraic Geometry
2010-05-19 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1005.3131,
title = {Higher-dimensional analogues of K3 surfaces},
author = {Kieran G. O'Grady},
journal= {arXiv preprint arXiv:1005.3131},
year = {2010}
}
Comments
The paper originated from a talk given at MSRI during the special program in Algebraic Geometry (2009).