Linear invariants of complex manifolds and their plurisubharmonic variations
文献类型：期刊论文
| 作者 | Deng, Fusheng2; Wang, Zhiwei3; Zhang, Liyou4; Zhou, Xiangyu1,2,5 |
| 刊名 | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| 出版日期 | 2020-07-15 |
| 卷号 | 279期号:1页码:27 |
| 关键词 | Linear isometry Plurisubharmonic variation Positivity of direct image sheaves Teichmuller metric |
| ISSN号 | 0022-1236 |
| DOI | 10.1016/j.jfa.2020.108514 |
| 英文摘要 | For a bounded domain D and a real number p > 0, denote by A(p) (D) the linear space of L-p integrable holomorphic functions on D, equipped with the L-p-pseudonorm. We prove that two bounded hyperconvex domains D-1 subset of C-n and D-2 subset of C-m are biholomorphic (in particular n = m) if there is a linear isometry between A(p) (D-1) and AP(D-2) for some 0 < p < 2. The same result holds for p > 2,p not equal 2,4, ..., provided that the p-Bergman kernels on D-1 and D-2 are exhaustive. With this as a motivation, we show that, for all p > 0, the p-Bergman kernel on a strongly pseudoconvex domain with C-2 boundary or a simply connected homogeneous regular domain is exhaustive. These results show that spaces of pluricanonical sections of complex manifolds equipped with canonical pseudonorms are important linear invariants of complex manifolds. The second part of the present work devotes to studying variations of these invariants. We show that the direct image sheaf of the twisted relative pluricanonical bundle associated to a holomorphic family of Stein manifolds or compact Kahler manifolds is positively curved, with respect to the canonical singular Finsler metric. (C) 2020 Elsevier Inc. All rights reserved. |
| 资助项目 | NSFC[NSFC-11871451] ; NSFC[NSFC-11701031] ; NSFC[NSFC-11671270] ; NSFC[NSFC-11688101] ; University of Chinese Academy of Sciences ; Beijing Natural Science Foundation[1202012] ; Beijing Natural Science Foundation[Z190003] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000526812300001 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51181]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wang, Zhiwei; Zhou, Xiangyu |
| 作者单位 | 1.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 4.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China 5.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Deng, Fusheng,Wang, Zhiwei,Zhang, Liyou,et al. Linear invariants of complex manifolds and their plurisubharmonic variations[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2020,279(1):27. |
| APA | Deng, Fusheng,Wang, Zhiwei,Zhang, Liyou,&Zhou, Xiangyu.(2020).Linear invariants of complex manifolds and their plurisubharmonic variations.JOURNAL OF FUNCTIONAL ANALYSIS,279(1),27. |
| MLA | Deng, Fusheng,et al."Linear invariants of complex manifolds and their plurisubharmonic variations".JOURNAL OF FUNCTIONAL ANALYSIS 279.1(2020):27. |
入库方式： OAI收割
来源：数学与系统科学研究院
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