On the decomposition of kähler manifolds with trivial canonical class

F. A. Bogomolov

doi:10.1070/SM1974v022n04ABEH001706

On the decomposition of kähler manifolds with trivial canonical class

F. A. Bogomolov

Mathematics

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Abstract

In this paper it is proved that simply-connected Kähler manifolds with K = 0 may be decomposed into a product Mⁿ = A^s K₃^m₁...K₃^m_kwhere h^{2, 0}(A^s) = 0, h;^{2, 0}(K₃^m_i) = 1 and the form Ω_i(2, 0) has maximal rank. Also the manifolds with l (K) > 1, of unirational type K = 0, are described. They may be presented as L^k/G, where K(L^k) = 0 and G is a finite group of birational automorphisms of L^k.

Original language	English (US)
Pages (from-to)	580-583
Number of pages	4
Journal	Mathematics of the USSR - Sbornik
Volume	22
Issue number	4
DOIs	https://doi.org/10.1070/SM1974v022n04ABEH001706
State	Published - Apr 30 1974

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title = "On the decomposition of k{\"a}hler manifolds with trivial canonical class",

abstract = "In this paper it is proved that simply-connected K{\"a}hler manifolds with K = 0 may be decomposed into a product Mn = As K3m1...K3mkwhere h2, 0(As) = 0, h;2, 0(K3mi) = 1 and the form Ωi(2, 0) has maximal rank. Also the manifolds with l (K) > 1, of unirational type K = 0, are described. They may be presented as Lk/G, where K(Lk) = 0 and G is a finite group of birational automorphisms of Lk.",

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AB - In this paper it is proved that simply-connected Kähler manifolds with K = 0 may be decomposed into a product Mn = As K3m1...K3mkwhere h2, 0(As) = 0, h;2, 0(K3mi) = 1 and the form Ωi(2, 0) has maximal rank. Also the manifolds with l (K) > 1, of unirational type K = 0, are described. They may be presented as Lk/G, where K(Lk) = 0 and G is a finite group of birational automorphisms of Lk.

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On the decomposition of kähler manifolds with trivial canonical class

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