Remarks on automorphism and cohomology of finite cyclic coverings of projective spaces
文献类型：期刊论文
| 作者 | Lyu, Renjie2; Pan, Xuanyu1 |
| 刊名 | MATHEMATICAL RESEARCH LETTERS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000658573200007 |
| 出版者 | INT PRESS BOSTON, INC |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。