Related papers: Dynamics of automorphisms on projective complex ma…

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As…

Under the framework of dynamics on normal projective varieties by Kawamata, Nakayama and Zhang \cite{Kawamata85,Nakayama10,NZ09,NZ10,Zhang16}, Hu and the author \cite{HL21}, we may reduce Kawaguchi-Silverman conjecture for automorphisms $f$…

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal…

We show that, in any dimension greater than one, there are an abelian variety, a smooth rational variety and a Calabi-Yau manifold, with primitive birational automorphisms of first dynamical degree $>1$. We also show that there are smooth…

We study the automorphisms of compact K\"ahler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that…

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact K\"ahler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation…

Let $X_0$ be a smooth projective threefold which is Fano or which has Picard number $1$. Let $\pi :X\rightarrow X_0$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then…

We show the validity of two special cases of the four-dimensional Minimal Model Program in characteristic $p>5$: for contractions to $\mathbb{Q}$-factorial fourfolds and in families over curves ("semi-stable mmp"). We also provide their…

We prove two results about the natural representation of a group G of automorphisms of a normal projective threefold X on its second cohomology. We show that if X is minimal then G, modulo a normal subgroup of null entropy, is embedded as a…

Let $X$ be a smooth complex projective curve, and let $x\in X$ be a point. We compute the automorphism group of the moduli space of framed vector bundles on $X$ of rank $r \geq 2$ with a framing over $x$. It is shown that this automorphism…

In the present work we classify the relatively minimal 3-dimensional quasihomogeneous complex projective varieties under the assumption that the automorphism group is not solvable. By relatively minimal we understand varieties X having at…

Let $(M,P\nabla_M)$ be a compact projective manifold and $Aut(M,P\nabla_M)$ its group of automorphisms. The purpose of this paper is to study the topological properties of $(M,P\nabla_M)$ if $Aut(M,P\nabla_M))$ is not discrete by applying…

Suppose that $X$ is a smooth, projective threefold over $\mathbb C$ and that $\phi : X \to X$ is an automorphism of positive entropy. We show that one of the following must hold, after replacing $\phi$ by an iterate: i) the canonical class…

In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…

For the Calabi-Yau threefolds $X$ constructed by C. Schoen as fiber products of generic rational elliptic surfaces, we show that the action of the automorphism group of $X$ on the K\"ahler cone of $X$ has a rationally polyhedral fundamental…

In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of…

We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…

For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective…

Let $\pi :X\rightarrow \mathbb{P}^3$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then its first and second dynamical degrees are the same. We also construct many…

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is…