Relations between the Kahler cone and the balanced cone of a Kahler manifold

TL;DR

This paper investigates the relationship between the Kahler cone and the balanced cone of a Kahler manifold, focusing on the properties of a natural map and characterizing nef classes that are Kahler.

Contribution

It provides new insights into the injectivity and surjectivity of the map between the Kahler and balanced cones, and offers an analytic criterion for nef classes to be Kahler.

Findings

The natural map's injectivity and surjectivity are analyzed.

An analytic characterization of nef classes as Kahler is established.

The study advances understanding of cone structures in Kahler geometry.

Abstract

In this paper, we consider a natural map from the Kahler cone to the balanced cone of a Kahler manifold. We study its injectivity and surjecticity. We also give an analytic characterization theorem on a nef class being Kahler.