Nonalgebraic hyperkähler manifolds
Nonalgebraic hyperkähler manifolds
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 …