Open Access
July 2010 Nonalgebraic hyperkähler manifolds
Frédéric Campana, Keiji Oguiso, Thomas Peternell
J. Differential Geom. 85(3): 397-424 (July 2010). DOI: 10.4310/jdg/1292940689


We study the algebraic dimension $a(X)$ of a compact hyperkähler manifold of dimension $2n$. We show that $a(X)$ is at most $n$ unless $X$ is projective. If a compact Kähler 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 also gives structure results for ”generalised hyperkähler” manifolds and studies nef lines bundles.


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Frédéric Campana. Keiji Oguiso. Thomas Peternell. "Nonalgebraic hyperkähler manifolds." J. Differential Geom. 85 (3) 397 - 424, July 2010.


Published: July 2010
First available in Project Euclid: 21 December 2010

zbMATH: 1232.53042
MathSciNet: MR2739808
Digital Object Identifier: 10.4310/jdg/1292940689

Rights: Copyright © 2010 Lehigh University

Vol.85 • No. 3 • July 2010
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