Compact complex manifolds whose complement of an analytic subset is Kahler

2020/03/25 by Shimobe, Hirokazu
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.11207

Abstract

In this paper, we consider a class of balanced manifolds and provide a proof of a problem proposed by Silva-that compact complex manifolds that are Kahler outside an analytic subset are balanced. Next, as a special case of this theorem, we prove that compact complex manifolds which are Kahler outside a Kahler submanifold are class C. Finally, we prove that a blow up along a submanifold of Hironaka's examples are Kahler, and we establish that Hironaka's examples are examples of this theorem.

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