The limit of the Yang-Mills-Higgs flow on Higgs bundles

Jiayu Li; Xi Zhang

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arXiv · 1410.8268

The limit of the Yang-Mills-Higgs flow on Higgs bundles

Jiayu Li·Xi Zhang

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Abstract

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact K\"ahler manifold $(M, \omega )$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle.

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Jiayu Li, Xi Zhang. 2014-10-30. The limit of the Yang-Mills-Higgs flow on Higgs bundles. https://arxiv.org/abs/1410.8268

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