Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00209-018-2160-8
Title: Characterizations of toric varieties via polarized endomorphisms
Authors: Meng, Sheng 
Zhang, De-Qi 
Keywords: Science & Technology
Physical Sciences
Mathematics
Polarized endomorphism
Toric pair
Complexity
Issue Date: 1-Aug-2019
Publisher: SPRINGER HEIDELBERG
Citation: Meng, Sheng, Zhang, De-Qi (2019-08-01). Characterizations of toric varieties via polarized endomorphisms. MATHEMATISCHE ZEITSCHRIFT 292 (3-Apr) : 1223-1231. ScholarBank@NUS Repository. https://doi.org/10.1007/s00209-018-2160-8
Abstract: Let X be a normal projective variety and f: X→ X a non-isomorphic polarized endomorphism. We give two characterizations for X to be a toric variety. First we show that if X is Q-factorial and G-almost homogeneous for some linear algebraic group G such that f is G-equivariant, then X is a toric variety. Next we give a geometric characterization: if X is of Fano type and smooth in codimension 2 and if there is an f- 1-invariant reduced divisor D such that f| X\D is quasi-étale and KX+ D is Q-Cartier, then X admits a quasi-étale cover X~ such that X~ is a toric variety and f lifts to X~. In particular, if X is further assumed to be smooth, then X is a toric variety.
Source Title: MATHEMATISCHE ZEITSCHRIFT
URI: https://scholarbank.nus.edu.sg/handle/10635/234653
ISSN: 0025-5874
1432-1823
DOI: 10.1007/s00209-018-2160-8
Appears in Collections:Staff Publications
Elements

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
1702.07883v2.pdf175.76 kBAdobe PDF

OPEN

Pre-printView/Download

SCOPUSTM   
Citations

3
checked on Nov 25, 2022

Page view(s)

7
checked on Nov 17, 2022

Download(s)

1
checked on Nov 17, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.