Higher dimensional essential minima and equidistribution of cycles

Abstract

The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic. In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more fexibility on the arithmetic datum.