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Let $X$ be an $n$-dimensional normal projective variety of Kodaira dimension $\kappa$ and $G$ an abelian subgroup of automorphisms such that all elements of $G\backslash \{\mathrm{id}\}$ are of positive entropy. Dinh and Sibony showed that $G$ is actually free abelian of rank $\le n-\kappa-1$. In this paper, we show th...
Let $X$ be a Jacobian elliptic surface with finite Mordell-Weil group and exactly one reducible fiber. We prove that if $\chi(\mathcal O_X)\ge \rho(X)$, then the Mori cone of $X$ is simplicial. As an application, assuming additionally $q(X)=0$, we show that $X$ satisfies the bounded cohomology property (BCP): there exi...
Let $\pi: X\to \mathbb P^1$ be a semistable Jacobian elliptic surface over $\mathbb C$, and set $\chi=\chi(\mathcal O_X)\ge3$, so that $\kappa(X)=1$. Assume that the Mordell-Weil group of $\pi$ is finite and that $\pi$ has at least one reducible fiber, the reducible fibers being of types $I_{n_1},\cdots, I_{n_s}$. Rece...
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