ALGEBRAIC DYNAMICS ON COMPACT NORMAL VARIETIES

Abstract

In this thesis, we first generalize the equivariant minimal model program (EMMP) from the algebraic situation to the transcendental case and give a few dynamical characterizations of Q-complex tori. Second, as an application of the EMMP, we show that a rationally connected smooth projective variety X admitting an int-amplified endomorphism f is toric if one of the following holds: (1) f has totally invariant ramifications; (2) X is a Fano threefold; or (3) X is a Fano fourfold admitting a conic bundle structure. Finally, we study the (totally) invariant subvarieties and give optimal upper bounds under some further dynamical restrictions. The second part and the third part are based on some joint works with Jia, Matsuzawa, Meng, Shibata and Zhang.