On the decomposition of K\"ahler manifolds with trivial canonical class

F. A. Bogomolov

Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 580-583

Résumé

In this paper it is proved that simply-connected Kähler manifolds with $K=0$ may be decomposed into a product $M^n=A^s\times K^{m_1}_3\times\cdots\times K^{m_k}_3$, where $h^{2,0}(A^s)=0$, $h^{2,0}(K^{m_i}_3)=1$ and the form $\omega_i(2,0)$ 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 $L^k$. Bibliography: 5 titles.