2017/04/26 by Hsueh-Yung Lin, Lin, Hsueh-Yung · 1 citation
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1704.08109
We prove that every compact Kähler threefold X of Kodaira dimension κ= 0 or 1 has a Q-factorial bimeromorphic model X' with at worst terminal singularities such that for each curve C ⊂ X', the pair (X',C) admits a locally trivial algebraic approximation such that the restriction of the deformation of X' to some neighborhood of C is a trivial deformation. As an application, we prove that every compact Kähler threefold with κ= 0 or 1 has an algebraic approximation.