The gradient flow of Higgs pairs

doi:10.4171/JEMS/284

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	The gradient flow of Higgs pairs
	Li, Jiayu2,3 ; Zhang, Xi 1
	2011
发表期刊	JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN	1435-9855
卷号	13 期号:5 页码:1373-1422
摘要	We consider the gradient flow of the Yang-Mills-Higgs functional of Higgs pairs on a Hermitian vector bundle (E, H-0) over a Kahler surface (M, omega), 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 (A(0), phi(0)) converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point (A(infinity,) phi(infinity)) of this functional. We also prove that the limiting Higgs pair (A(infinity), phi(infinity)) can be extended smoothly to a vector bundle E-infinity over (M, omega) and the isomorphism class of the limiting Higgs bundle (E-infinity, A(infinity), phi(infinity)) is given by the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle (E, A(0), phi(0)).
关键词	Higgs bundles Kahler surface Harder-Narasimhan-Seshadri filtration
DOI	10.4171/JEMS/284
语种	英语
资助项目	NSF in China[10771188] ; Ministry of Education[20060335133]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000295714100006
出版者	EUROPEAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11817
专题	数学所
通讯作者	Zhang, Xi
作者单位	1.Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China 2.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China 3.Chinese Acad Sci, AMSS, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Li, Jiayu,Zhang, Xi. The gradient flow of Higgs pairs[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,2011,13(5):1373-1422.
APA	Li, Jiayu,&Zhang, Xi.(2011).The gradient flow of Higgs pairs.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,13(5),1373-1422.
MLA	Li, Jiayu,et al."The gradient flow of Higgs pairs".JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 13.5(2011):1373-1422.