Non-algebraic Hyperkaehler manifolds

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.

18 pages

References in corpus (3)

• Base point free theorems--saturation, b-divisors, and canonical bundle formula--
• Fibrations meromorphes sur certaines varietes de classe canonique triviale
• Effective Iitaka fibrations

Cited by in corpus (4)

• Kobayashi pseudometric on hyperkahler manifolds
• Versions of injectivity and extension theorems
• Parabolic nef currents on hyperkaehler manifolds
• Hyperkahler SYZ conjecture and semipositive line bundles