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Title: Invariant Subvarieties With Small Dynamical Degree
Authors: Matsuzawa, Y
Meng, S 
Shibata, T 
Zhang, DQ 
Zhong, G
Keywords: math.AG
14J50, 08A35, 32H50, 37B40, 11G10, 14M25
Issue Date: 1-Jul-2022
Publisher: Oxford University Press (OUP)
Citation: Matsuzawa, Y, Meng, S, Shibata, T, Zhang, DQ, Zhong, G (2022-07-01). Invariant Subvarieties With Small Dynamical Degree. International Mathematics Research Notices 2022 (15) : 11448-11483. ScholarBank@NUS Repository.
Abstract: Let f : X → X be a dominant self-morphism of an algebraic variety. Consider the set ∑f8 of f -periodic subvarieties of small dynamical degree (SDD), the subset Sf8 of maximal elements in ∑f8, and the subset Sf of f -invariant elements in Sf8. When X is projective, we prove the finiteness of the set Pf of f -invariant prime divisors with SDD and give an optimal upper bound Pf n = d1(f )n(1 + o(1)) as n→8, where d1(f ) is the 1st dynamic degree. When X is an algebraic group (with f being a translation of an isogeny), or a (not necessarily complete) toric variety, we give an optimal upper bound Sf n = d1(f )n dim(X)(1 + o(1)) as n→8, which slightly generalizes a conjecture of S.-W. Zhang for polarized f .
Source Title: International Mathematics Research Notices
ISSN: 1073-7928
DOI: 10.1093/imrn/rnab039
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