Calibrations modulo \(\nu\) (Q1822349)

The theory of calibrations has provided many families of m-dimensional area-minimizing surfaces. This paper introduces a theory of calibrations modulo \(\nu\), where \(\nu\) is an integer greater than one. It provides examples of surfaces minimizing m-dimensional area modulo \(\nu\). In the past such examples have been difficult to obtain. As an example, the techniques of this paper show that a complex algebraic variety in \(C^ n\) of degree d is area-minimizing modulo \(\nu\) for all \(\nu\geq 2d\).