English

Compact complex manifolds whose complement of an analytic subset is Kahler

Differential Geometry 2020-07-14 v2

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.

Keywords

Cite

@article{arxiv.2003.11207,
  title  = {Compact complex manifolds whose complement of an analytic subset is Kahler},
  author = {Hirokazu Shimobe},
  journal= {arXiv preprint arXiv:2003.11207},
  year   = {2020}
}

Comments

We think that the proofs of these are incorrect for elementary reasons

R2 v1 2026-06-23T14:26:22.575Z