A functorial lower bound for the essential minimum of varities in a power of an elliptic curve

Abstract

A subvariety V of an abelian variety is `translate' if it is the union of translates of proper algebraic subgroups. An irreducible V is `transverse' if it is not contained in any translate variety. Effective sharp lower bounds for a transverse subvarieties of a power of an elliptic curve E are known. Here, we prove a sharp lower bound for the essential minimum of non-translate subvarieties of such a power E^g.