Year: 2011
Type: preprint
Abstract: Compact hyperkaehler manifolds are higher-dimensional generalizations of K3 surfaces. The classical Global Torelli theorem for K3 surfaces, however, does not hold in higher dimensions. More precisely, a compact hyperkaehler manifold is in general not determined by its natural weight-two Hodge structure. The text gives an account of a recent theorem of M. Verbitsky, which can be regarded as a weaker version of the Global Torelli theorem phrased in terms of the injectivity of the period map on the connected components of the moduli space of marked manifolds.
Source: arXiv (Cornell University)
Author: Huybrechts, Daniel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1671891775