Let $X$ be a normal projective variety of dimension $n$ and $G$ an abelian group of automorphisms such that all elements of $G\setminus \{ \mathrm{ id}\}$ are of positive entropy. Dinh and Sibony showed that $G$ is actually free abelian of rank $\le n - 1$. The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\mathrm{ rank} G = n - 2$.
Categories: math.AG math.DS