Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/234644
Title: Polynomial log-volume growth in slow dynamics and the GK-dimensions of twisted homogeneous coordinate rings
Authors: Lin, Hsueh-Yung
Oguiso, Keiji
Zhang, De-Qi 
Keywords: math.AG
math.AG
math.DS
math.RA
14J50, 16P90, 16S38, 32H50, 37B40
Issue Date: 8-Apr-2021
Citation: Lin, Hsueh-Yung, Oguiso, Keiji, Zhang, De-Qi (2021-04-08). Polynomial log-volume growth in slow dynamics and the GK-dimensions of twisted homogeneous coordinate rings. ScholarBank@NUS Repository.
Abstract: Twisted homogeneous coordinate rings are natural invariants associated to a projective variety X with an automorphism f. We study the Gelfand-Kirillov dimensions of these noncommutative algebras from the perspective of complex dynamics, by noticing that when X is a smooth complex projective variety, they essentially coincide with the polynomial logarithmic volume growth Plov(f) of (X,f). We formulate some basic dynamical properties about these invariants and study explicit examples. Our main results are new upper bounds and lower bounds of these invariants, in terms of the dimension of X (as well as other refinements). As an application, we completely determine Plov(f) when dim X = 3.
URI: https://scholarbank.nus.edu.sg/handle/10635/234644
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