Non-algebraic Hyperkaehler manifolds

Details Non-algebraic Hyperkaehler manifolds Non-algebraic Hyperkaehler manifolds

2008-04-10

arxiv.org/abs/0804.1682v1

Mathematics

Differential Geometry

18 pages

Scientific paper

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.

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