KMS Of Academy of mathematics and systems sciences, CAS
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. |
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