Non-algebraic Hyperkaehler manifolds
Differential Geometry
2008-04-11 v1 Algebraic Geometry
Abstract
We study the algebraic dimension a(X) of a compact hyperkaehler manfold of dimension 2n. We show that a(X) is at most n unless X is projective. If a compact Kaehler manifold with algebraic dimension 0 and Kodaira dimension 0 has a minimal model, then only the values 0,n and 2n are possible. In case of middle dimension, the algebraic reduction is holomorphic Lagrangian. If n = 2, then - without any assumptions - the algebraic dimension only takes the values 0,2 and 4. The paper gives structure results for "generalised hyperkaehler" manifolds and studies nef lines bundles.
Cite
@article{arxiv.0804.1682,
title = {Non-algebraic Hyperkaehler manifolds},
author = {Frederic Campana and Keiji Oguiso and Thomas Peternell},
journal= {arXiv preprint arXiv:0804.1682},
year = {2008}
}
Comments
18 pages