o-minimal flows on abelian varieties

Abstract

Let $A$ be an abelian variety over $\mathbf{C}$ of dimension $n$ and $\pi :{\mathbf{C}}^n\to A$ be the complex uniformisation. Let $X$ be an unbounded subset of ${\mathbf{C}}^n$ definable in a suitable o-minimal structure. We give a description of the Zariski closure of $\pi (X)$.