Please use this identifier to cite or link to this item: https://doi.org/10.4310/MRL.2020.v27.n2.a8
Title: Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism
Authors: Meng, Sheng 
Zhang, De-Qi 
Keywords: Science & Technology
Physical Sciences
Mathematics
Issue Date: 1-Jan-2020
Publisher: INT PRESS BOSTON, INC
Citation: Meng, Sheng, Zhang, De-Qi (2020-01-01). Semi-group structure of all endomorphisms of a projective variety admitting a polarized endomorphism. MATHEMATICAL RESEARCH LETTERS 27 (2) : 523-549. ScholarBank@NUS Repository. https://doi.org/10.4310/MRL.2020.v27.n2.a8
Abstract: Let X be a projective variety admitting a polarized (or more generally, int-amplified) endomorphism. We show: there are only finitely many contractible extremal rays; and when X is Q-factorial normal, every minimal model program is equivariant relative to the monoid SEnd(X) of all surjective endomorphisms, up to finite index. Further, when X is rationally connected and smooth, we show: there is a finite-index submonoid G of SEnd(X) such that G acts via pullback as diagonal (and hence commutative) matrices on the Neron-Severi group; the full automorphisms group Aut(X) has finitely many connected components; and every amplified endomorphism is int-amplified.
Source Title: MATHEMATICAL RESEARCH LETTERS
URI: https://scholarbank.nus.edu.sg/handle/10635/234651
ISSN: 1073-2780
1945-001X
DOI: 10.4310/MRL.2020.v27.n2.a8
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