Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/135442
Title: ON AUTOMORPHISM GROUPS OF ALGEBRAIC VARIETIES - A DYNAMICAL VIEWPOINT
Authors: HU FEI
Keywords: automorphism group, topological entropy, dynamical degree, maximal dynamical rank, semi-abelian variety, group action
Issue Date: 13-Jan-2017
Source: HU FEI (2017-01-13). ON AUTOMORPHISM GROUPS OF ALGEBRAIC VARIETIES - A DYNAMICAL VIEWPOINT. ScholarBank@NUS Repository.
Abstract: Throughout this thesis, we work over the field C of complex numbers. My thesis contains the following three parts. 1. We generalized a surface result, that is, a parabolic automorphism of a compact Kähler surface preserves an elliptic fibration, to hyperkähler manifolds. We gave a criterion for the existence of equivariant fibrations on hyperkähler manifolds from a dynamical viewpoint. 2. We studied virtually solvable groups G of maximal dynamical rank acting on a compact Kähler manifold X. Based on the known Tits alternative type theorem of Zhang (2009), we generalized a finiteness result for the null-entropy subset of a commutative automorphism group due to Dinh–Sibony (2004). We then determined positive-dimensional G-periodic proper subvarieties of the pair (X, G) of maximal dynamical rank. Actually, among other results, we proved that the union of all these positive-dimensional G-periodic proper subvarieties is a Zariski closed subset of X. 3. An upper bound about the dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors was obtained. In dimension two, I generalized a classical result of Iitaka for logarithmic Iitaka surfaces to arbitrary algebraic surfaces of logarithmic Kodaira dimension 0.
URI: http://scholarbank.nus.edu.sg/handle/10635/135442
Appears in Collections:Ph.D Theses (Open)

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