Free abelian group actions on normal projective varieties: sub-maximal dynamical rank case

Abstract

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 $\mathrm{rank}G=n-2$.

to appear in Canad. J. Math., minor revision