Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces

	Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces
	Lyu, Renjie 2; Pan, Xuanyu 1
刊名	MATHEMATICAL RESEARCH LETTERS
	2021
卷号	28 期号:3 页码:785-822
ISSN号	1073-2780
英文摘要	For a smooth finite cyclic covering over a projective space of dimension greater than one, we show that its group of automorphisms faithfully acts on its cohomology except for a few cases. In characteristic zero, we study the equivariant deformation theory and groups of automorphisms for complex cyclic coverings. The proof uses the decomposition of the sheaf of differential forms due to Esnault and Viehweg. In positive characteristic, a lifting criterion of automorphisms reduce the faithfulness problem to characteristic zero. To apply this criterion, we prove the degeneration of the Hodge-de Rham spectral sequences for a family of smooth finite cyclic coverings, and the infinitesimal Torelli theorem for finite cyclic coverings defined over an arbitrary field.
WOS研究方向	Mathematics
语种	英语
出版者	INT PRESS BOSTON, INC
WOS记录号	WOS:000658573200007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58782]
专题	中国科学院数学与系统科学研究院
通讯作者	Lyu, Renjie
作者单位	1.Chinese Acad Sci, AMSS, Inst Math, 55 ZhongGuanCun East Rd, Beijing 100190, Peoples R China 2.Univ Amsterdam, Korteweg de Vries Inst, Sci Pk 105-107, NL-1098 XG Amsterdam, Netherlands
推荐引用方式 GB/T 7714	Lyu, Renjie,Pan, Xuanyu. Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces[J]. MATHEMATICAL RESEARCH LETTERS,2021,28(3):785-822.
APA	Lyu, Renjie,&Pan, Xuanyu.(2021).Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces.MATHEMATICAL RESEARCH LETTERS,28(3),785-822.
MLA	Lyu, Renjie,et al."Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces".MATHEMATICAL RESEARCH LETTERS 28.3(2021):785-822.