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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 |
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