Kobayashi pseudometric on hyperkähler manifolds (Q2922846)
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scientific article; zbMATH DE number 6355579
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kobayashi pseudometric on hyperkähler manifolds |
scientific article; zbMATH DE number 6355579 |
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Kobayashi pseudometric on hyperkähler manifolds (English)
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15 October 2014
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hyper-Kähler manifolds
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Kobayashi pseudometric
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Lagrangian fibrations
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abelian fibrations
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\textit{S. Kobayashi} conjectured that projective manifolds with trivial canonical bundle have vanishing Kobayashi pseudometric [Bull. Am. Math. Soc. 82, 357--416 (1976; Zbl 0346.32031)]. The main aim of the paper is to prove this conjecture for hyper-Kähler manifolds with \(b_2\geq 7\) admitting a deformation with a Lagrangian fibration and whose Picard rank is not maximal. As a corollary the authors prove Kobayashi's conjecture for all K3 surfaces and their Hilbert schemes.
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