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	THE PICARD GROUP OF THE LOOP SPACE OF THE RIEMANN SPHERE
	Zhang, Ning
	2010
关键词	Loop space holomorphic line bundle Picard group projective embedding Dolbeault cohomology group
英文摘要	The loop space LP(1) of the Riemann sphere consisting of all C(k) or Sobolev W(k,p) maps S(1) -> P(1) is an infinite dimensional complex manifold. We compute the Picard group Pic(LP(1)) of holomorphic line bundles on LP(1) as an infinite dimensional complex Lie group with Lie algebra the Dolbeault group H(0,1)(LP(1)). The group G of Mobius transformations and its loop group LG act on LP(1). We prove that an element of Pic(LP(1)) is LG-fixed if it is G-fixed, thus completely answering the question of Millson and Zombro about the G-equivariant projective embedding of LP(1).; Mathematics; SCI(E); 0; ARTICLE; 11; 1387-1399; 21
语种	英语
出处	SCI
出版者	international journal of mathematics
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/395261]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhang, Ning. THE PICARD GROUP OF THE LOOP SPACE OF THE RIEMANN SPHERE. 2010-01-01.

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