Periodic subvarieties of a projective variety under the action of a   maximal rank abelian group of positive entropy
  We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy. The motivation of the paper is to understand the obstruction for X to be G-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group. 
Fei Hu, Sheng-Li Tan and De-Qi Zhang
math.AG math.DS