The limits of Kahler manifolds under holomorphic deformations

TL;DR

This paper proves that Kahler manifolds remain Kahler under holomorphic deformations given mild metric and topological assumptions on the central fiber.

Contribution

It establishes the stability of Kahler property under holomorphic deformations with specific mild assumptions.

Findings

Kahler manifolds are stable under certain holomorphic deformations.

The result depends on mild assumptions on the metric and topology.

The limit of Kahler manifolds remains Kahler under these conditions.

Abstract

With some mild assumptions on metric and topology of the central fiber, we prove that the limit of Kahler manifolds under holomorphic deformation is still Kahler.