Algebraic approximations of compact Kähler threefolds of Kodaira dimension 0 or 1

Abstract

We prove that every compact Kähler threefold $X$ of Kodaira dimension $\kappa =0$ or $1$ has a $\mathbf{Q}$-factorial bimeromorphic model $X^{\prime }$ with at worst terminal singularities such that for each curve $C\subset X^{\prime }$, the pair $(X^{\prime },C)$ admits a locally trivial algebraic approximation such that the restriction of the deformation of $X^{\prime }$ to some neighborhood of $C$ is a trivial deformation. As an application, we prove that every compact Kähler threefold with $\kappa =0$ or $1$ has an algebraic approximation.

Minor modifications; Proposition 1.7 added. Comments are welcome

Cited by in corpus (1)

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