Stability of the tangent bundles of complete intersections and effective restriction

	Stability of the tangent bundles of complete intersections and effective restriction
	Liu, Jie
刊名	ANNALES DE L INSTITUT FOURIER
	2021
卷号	71 期号:3 页码:1601-1634
关键词	stability tangent bundle Lefschetz property complete intersection Hermitian symmetric space
ISSN号	0373-0956
英文摘要	For n >= 3 and r >= 1, let M be an (n r)-dimensional irreducible Hermitian symmetric space of compact type and let O-M (1) be the ample generator of pic(M). Let Y = H-1 boolean AND center dot center dot center dot&ANDH(r) be a smooth complete intersection of dimension n, where H-i is an element of vertical bar O-M (d(i))vertical bar with di >= 2. We prove a vanishing theorem for twisted holomorphic forms on Y. As an application, we show that the tangent bundle T-Y of Y is stable. Moreover, if X is a smooth hypersurface of degree d in Y such that the restriction pic(Y) -> pic(X) is surjective, we establish some effective results for d to guarantee the stability of the restriction T-Y vertical bar(X). In particular, if Y is a general hypersurface in Pn+1 and X is a general smooth divisor in Y, we show that T-Y vertical bar(X) is stable except for some well-known examples. We also address the cases where the Picard group increases by restriction.
WOS研究方向	Mathematics
语种	英语
出版者	ANNALES INST FOURIER
WOS记录号	WOS:000772480200017
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60221]
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Jie
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Jie. Stability of the tangent bundles of complete intersections and effective restriction[J]. ANNALES DE L INSTITUT FOURIER,2021,71(3):1601-1634.
APA	Liu, Jie.(2021).Stability of the tangent bundles of complete intersections and effective restriction.ANNALES DE L INSTITUT FOURIER,71(3),1601-1634.
MLA	Liu, Jie."Stability of the tangent bundles of complete intersections and effective restriction".ANNALES DE L INSTITUT FOURIER 71.3(2021):1601-1634.