A note of semistable Higgs bundles over compact K\"ahler manifolds
Yanci Nie, Xi Zhang
TL;DR
This paper demonstrates that semistable Higgs bundles with zero first and second Chern numbers over compact Kähler manifolds can be filtered into Hermitian flat Higgs bundles using the Yang-Mills-Higgs flow.
Contribution
It establishes a new structural result linking semistability, Chern number vanishing, and Hermitian flatness via the Yang-Mills-Higgs flow.
Findings
Semistable Higgs bundles with vanishing Chern numbers admit a specific filtration.
The filtration's quotients are Hermitian flat Higgs bundles.
The Yang-Mills-Higgs flow is used to prove the existence of this filtration.
Abstract
In this note, by using the Yang-Mills-Higgs flow, we show that semistable Higgs bundles with vanishing the first and second Chern numbers over compact K\"aher manifolds must admit a filtration whose quotients are Hermitian flat Higgs bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry