PERIODIC SUBVARIETIES OF A PROJECTIVE VARIETY UNDER THE ACTION OF A MAXIMAL RANK ABELIAN GROUP OF POSITIVE ENTROPY

Abstract

We determine positive-dimensional G-periodic proper subvarieties of an ndimensional 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.