2012/11/09 by Junyan Cao, Cao, Junyan
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1211.2058
It has been shown by Claire Voisin in 2003 that one cannot always deform a compact Kähler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an additional semipositivity or seminegativity condition on the canonical bundle, the answer becomes positive, namely such a compact Kähler manifold can be approximated by deformations of projective manifolds.