Note on quasi-polarized canonical Calabi-Yau threefolds

doi:10.5802/crmath.55

	Note on quasi-polarized canonical Calabi-Yau threefolds
	Liu, Jie
刊名	COMPTES RENDUS MATHEMATIQUE
	2020
卷号	358 期号:4 页码:415-420
关键词	birationality Calabi-Yau threefolds Fano manifolds freeness
ISSN号	1631-073X
DOI	10.5802/crmath.55
英文摘要	Let (X, L) be a quasi-polarized canonical Calabi-Yau threefold. In this note, we show that vertical bar mL vertical bar is basepoint free form m >= 4. Moreover, if the morphism Phi(vertical bar 4L vertical bar) is not birational onto its image and h(0) (X,L) >= 2, then L-3 = 1. As an application, if Y is an n-dimensional Fano manifold such that -K-Y = (n - 3)H for some ample divisor H, then vertical bar mH vertical bar is basepoint free form m >= 4 and if the morphism Phi(vertical bar 4H vertical bar) is not birational onto its image, then either Y is a weighted hypersurface of degree 10 in the weighted projective space P(1, ..., 1,2,5) or h(0) (Y, H) = n - 2.
WOS研究方向	Mathematics
语种	英语
出版者	centre Mersenne pour ldition scientifique ouverte
WOS记录号	WOS:000573976500004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52263]
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Jie
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Jie. Note on quasi-polarized canonical Calabi-Yau threefolds[J]. COMPTES RENDUS MATHEMATIQUE,2020,358(4):415-420.
APA	Liu, Jie.(2020).Note on quasi-polarized canonical Calabi-Yau threefolds.COMPTES RENDUS MATHEMATIQUE,358(4),415-420.
MLA	Liu, Jie."Note on quasi-polarized canonical Calabi-Yau threefolds".COMPTES RENDUS MATHEMATIQUE 358.4(2020):415-420.