Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities

doi:10.1007/s00208-021-02275-7

	Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
	Wang, Juanyong 1,2
刊名	MATHEMATISCHE ANNALEN
	2022-10-01
卷号	384 期号:1-2 页码:47-100
ISSN号	0025-5831
DOI	10.1007/s00208-021-02275-7
英文摘要	In this article we study the structure of klt projective varieties with nef anticanonical divisor (and more generally, varieties of semi-Fano type), especially the canonical fibrations associated to them. We show that - The Albanese map for such variety is a locally constant fibration (that is, a locally trivial fibration such that X is isomorphic to the product of the universal cover of the Albanese torus by the fibre of the Albanese map quotient by a diagonal action of the fundamenatl group of the Albanese torus). - If the smooth locus is simply connected, the MRC fibration of such variety is an everywhere defined morphism and induces a decomposition of this variety into a product of a rationally connected variety by a projective variety with trivial canonical divisor. These generalize the corresponding results for smooth projective varieties with nef anticanonical bundle inCao (2019) and Cao-Horing (2019) to the klt case, and partially reduce the structure problem of these varieties to the singular Beauville-Bogomolov decomposition theorem proved by successive works of Greb-Kebekus-Peternell (2016), Druel (2018), Guenencia-Greb-Kebekus (2019) and Horing-Peternell (2019).
资助项目	French 'Agence nationale de recherche' (ANR)
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000849363900013
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60995]
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Juanyong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 55 Rd Zhongguancun, Beijing 100190, Peoples R China 2.Ecole Polytech, CMLS, F-91128 Palaiseau, France
推荐引用方式 GB/T 7714	Wang, Juanyong. Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities[J]. MATHEMATISCHE ANNALEN,2022,384(1-2):47-100.
APA	Wang, Juanyong.(2022).Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities.MATHEMATISCHE ANNALEN,384(1-2),47-100.
MLA	Wang, Juanyong."Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities".MATHEMATISCHE ANNALEN 384.1-2(2022):47-100.