Colloquium| Institute of Mathematical Sciences
Time：Tuesday, December 13rd, 2022, 13:30-14:30
Location：RS408, IMS
Speaker: Chen Jiang, SCMS Fudan University
Abstract: For an automorphism f of a smooth projective variety X, Gromov introduced the log-volume growth of f and showed that it coincides with the algebraic/topological entropy of f. In order to study automorphisms of zero entropy, Cantat and Paris-Romaskevich introduced polynomial log-volume growth of f (plov for short) which turns out to be closely related to the Gelfand—-Kirillov dimension of the twisted homogeneous coordinate ring associated with (X, f). We show an optimal upper bound that plov(f) is at most d^2, where d is the dimension of X. This affirmatively answers questions of Cantat--Paris--Romaskevich and Lin--Oguiso--Zhang. This is joint work with Fei Hu.