Hitchin's connection and differential operators with values in the determinant bundle

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	Hitchin's connection and differential operators with values in the determinant bundle
	Sun, XT ; Tsai, IH
	2004-06-01
发表期刊	JOURNAL OF DIFFERENTIAL GEOMETRY
ISSN	0022-040X
卷号	67 期号:2 页码:335-376
摘要	For a family of smooth curves, we have the associated family of moduli spaces of stable bundles with fixed determinant on the curves. There exists a so called theta line bundle on the family of moduli spaces. When the Kodaira-Spencer map of the family of curves is an isomorphism, we prove in this paper an identification theorem between sheaves of differential operators on the theta line bundle and higher direct images of vector bundles on curves. As an application, the so called Hitchin's connection on the direct image of (powers of) theta line bundle is derived naturally from the identification theorem. A logarithmic extension of Hitchin's connection to certain singular stable curves is also presented in this paper.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000230835700005
出版者	INT PRESS BOSTON, INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/666
专题	中国科学院数学与系统科学研究院
通讯作者	Sun, XT
作者单位	1.Chinese Acad Sci, Inst Math, AMSS, Beijing 100864, Peoples R China 2.Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China 3.Natl Taiwan Univ, Dept Math, Taipei, Taiwan
推荐引用方式 GB/T 7714	Sun, XT,Tsai, IH. Hitchin's connection and differential operators with values in the determinant bundle[J]. JOURNAL OF DIFFERENTIAL GEOMETRY,2004,67(2):335-376.
APA	Sun, XT,&Tsai, IH.(2004).Hitchin's connection and differential operators with values in the determinant bundle.JOURNAL OF DIFFERENTIAL GEOMETRY,67(2),335-376.
MLA	Sun, XT,et al."Hitchin's connection and differential operators with values in the determinant bundle".JOURNAL OF DIFFERENTIAL GEOMETRY 67.2(2004):335-376.