Semistable Higgs bundles over compact Gauduchon manifolds
Yanci Nie, Xi Zhang
TL;DR
This paper investigates the relationship between approximate Hermitian-Einstein structures and semi-stability of Higgs bundles over compact Gauduchon manifolds, establishing their equivalence through the continuity method.
Contribution
It proves the equivalence between approximate Hermitian-Einstein structures and semi-stability for Higgs bundles on compact Gauduchon manifolds, a novel result in this setting.
Findings
Equivalence between approximate Hermitian-Einstein structures and semi-stability.
Use of the continuity method to establish the equivalence.
Extension of known results to Gauduchon manifolds.
Abstract
In this paper, we consider the existence of approximate Hermitian-Einstein structure and the semi-stability on Higgs bundles over compact Gauduchon manifolds. By using the continuity method, we show that they are equivalent.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows