The gradient flow of Higgs pairs

• Autores: Jiayu Li, Xi Zhang
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 13, Nº 5, 2011, págs. 1373-1422
• Idioma: inglés
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• Resumen

  • In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional of Higgs pairs on a Hermitian vector bundle (E,H0) over a Kähler surface (M,?), and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition (A0,?0) converges, in an appropriate sense which takes into account bubbling phenomena, to a critical points (A?,??) of this functional. We also prove that the limiting Higgs pair (A?,??) can be extended smoothly to a vector bundle E? over (M,?) , and the isomorphism class of the limiting Higgs bundle (E?,A?,??) is given by the double dual of the graded Higgs sheaves associate to Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle (E,A0,?0).