The holomorphic limit of Kahler manifolds

TL;DR

This paper investigates the deformation limits of compact Kahler manifolds, establishing conditions for limits to be in Fujiki class C and proving a special case of the Streets-Tian conjecture.

Contribution

It provides a characterization of deformation limits in terms of volume finiteness and confirms the Streets-Tian conjecture in a specific scenario.

Findings

Limit in Fujiki class C iff upper volume is finite

Proved Streets-Tian conjecture for a special case

Characterized deformation limits of Kahler manifolds

Abstract

In this paper, we study the deformation limit of compact Kahler manifolds. We show that the limit to be a manifold in the Fujiki class C is equivalent to the finiteness of the upper volume. We also prove the Streets-Tian conjecture for a special case.