Stability of the tangent bundles of complete intersections and effective restriction

CSpace

	Stability of the tangent bundles of complete intersections and effective restriction
	Liu, Jie
	2021
发表期刊	ANNALES DE L INSTITUT FOURIER
ISSN	0373-0956
卷号	71 期号:3 页码:1601-1634
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.
关键词	stability tangent bundle Lefschetz property complete intersection Hermitian symmetric space
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000772480200017
出版者	ANNALES INST FOURIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60222
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.