Green currents for modular cycles in arithmetic quotients of complex hyperballs (Q996144)

Given an analytic subvariety \(Y\) of a complex manifold \(X\) of codimension \(r\), the Green current for \(Y\) is a current \(\mathcal G\) of \((r-1, r-1)\)-type on \(X\) such that \(d d^c \mathcal G + \delta_Y\) is represented by a \(C^\infty\)-form of \((r,r)\)-type on \(X\). In the arithmetic intersection theory developed by Gillet and Soulé, the role played by algebraic cycles in the usual intersection theory is replace by arithmetic cycles. In this paper the author obtains a Green current on an arithmetic quotient of a complex hyperball for a modular cycle stemming from a complex subhyperball of codimension greater than one, generalizing the classical construction of automorphic Green functions for modular curves.