KMS Of Academy of mathematics and systems sciences, CAS
| Linear invariants of complex manifolds and their plurisubharmonic variations | |
| Deng, Fusheng1; Wang, Zhiwei2; Zhang, Liyou3; Zhou, Xiangyu1,4,5 | |
| 2020-07-15 | |
| Source Publication | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| ISSN | 0022-1236 |
| Volume | 279Issue:1Pages:27 |
| Abstract | 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. |
| Keyword | Linear isometry Plurisubharmonic variation Positivity of direct image sheaves Teichmuller metric |
| DOI | 10.1016/j.jfa.2020.108514 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000526812300001 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51182 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Wang, Zhiwei; Zhou, Xiangyu |
| Affiliation | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 3.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China 4.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China |
| Recommended Citation 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. |
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