Flat Higgs bundles over non-compact affine Gauduchon manifolds
Zhenghan Shen, Chuanjing Zhang, Xi Zhang
TL;DR
This paper extends the Donaldson-Uhlenbeck-Yau theorem to flat Higgs bundles on non-compact affine Gauduchon manifolds using the affine Hermitian-Yang-Mills flow, broadening the understanding of stability conditions in complex geometry.
Contribution
It introduces a generalized theorem for flat Higgs bundles on non-compact affine Gauduchon manifolds, utilizing the affine Hermitian-Yang-Mills flow.
Findings
Proves a generalized Donaldson-Uhlenbeck-Yau theorem.
Establishes stability conditions for flat Higgs bundles.
Develops techniques for non-compact affine manifolds.
Abstract
In this paper, we use the affine Hermitian-Yang-Mills flow to prove a generalized Donaldson-Uhlenbeck-Yau theorem on flat Higgs bundles over a class of non-compact affine Gauduchon manifolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology