On the linearization stability of the Chern-scalar curvature

TL;DR

This paper investigates the local behavior of the Chern-scalar curvature function, focusing on its linearization stability and the structure of Hermitian metrics with a given curvature.

Contribution

It provides new insights into the linearization stability of the Chern-scalar curvature and characterizes the space of Hermitian metrics with prescribed curvature.

Findings

Established conditions for linearization stability of Chern-scalar curvature

Described the structure of the space of Hermitian metrics with prescribed curvature

Identified local properties of the curvature function

Abstract

In this note, we study the local properties of the Chern-scalar curvature function by looking at its linearization. In particular, we study its linearization stability and the structure of the space of Hermitian metrics with prescribed Chern-scalar curvature.