arXiv subjects

Hirokazu Shimobe

Publications and source records attributed to Hirokazu Shimobe.

2 recordsLinked to original sources

arXiv2020

Compact complex manifolds whose complement of an analytic subset is Kahler

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.

math.DG↗

arXiv2019

A small deformation and modifications of locally conformally balanced manifolds

We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to locally conformally balanced manifolds by Hilbert-Chow map.

math.DG↗