On the Toda systems of VHS type

TL;DR

This paper studies Toda systems of VHS type with singularities, establishing criteria for solution existence with specific asymptotics and proving their uniqueness using Higgs-Hermitian-Yang-Mills metrics and stability theory.

Contribution

It introduces a criterion for existence and uniqueness of solutions to Toda systems of VHS type with singular sources, leveraging Simpson's stability theory.

Findings

Established a criterion for solution existence with prescribed asymptotics.

Proved the uniqueness of solutions for Toda systems of VHS type.

Applied Simpson's theory to connect stability with solution construction.

Abstract

We consider the Toda systems of VHS type with singular sources and provide a criterion for the existence of solutions with prescribed asymptotic behaviour near singularities. We also prove the uniqueness of solution. Our approach uses Simpson's theory of constructing Higgs-Hermitian-Yang-Mills metrics from stability.