Non-algebraic Hyperkaehler manifolds

Campana, Frederic; Oguiso, Keiji; Peternell, Thomas

Non-algebraic Hyperkaehler manifolds

Authors

Campana, Frederic

Oguiso, Keiji

Peternell, Thomas

Description

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.
18 pages