Expansive subdynamics for algebraic Z^d-actions

A general framework for investigating topological actions of Zd on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower dimensional subspaces of Rd. Here we completely describe this expansive behavior for the class of Zd-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an algebraic variety together with a directional version of Noetherian modules over the ring of Laurent polynomials in several commuting variables.