Linear invariants of complex manifolds and their plurisubharmonic variations

doi:10.1016/j.jfa.2020.108514

CSpace

	Linear invariants of complex manifolds and their plurisubharmonic variations
	Deng, Fusheng 1; Wang, Zhiwei 2; Zhang, Liyou 3; Zhou, Xiangyu 1,4,5
	2020-07-15
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	279 期号:1 页码:27
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.
关键词	Linear isometry Plurisubharmonic variation Positivity of direct image sheaves Teichmuller metric
DOI	10.1016/j.jfa.2020.108514
收录类别	SCI
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000526812300001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51182
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.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
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.