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The limit of the Yang-Mills-Higgs flow for twisted Higgs pairs

Changpeng Pan,Zhenghan Shen,Pan Zhang

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS（2024）

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Abstract
In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over Kahler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension 4, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial twisted Higgs bundle.
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Yang-Mills-Higgs flow,twisted Higgs pair,Harder-Narasimhan-Seshadri filtration
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