Convexity properties for cycle spaces (Q1396298)

The authors study several properties of the space \(\mathcal{C}_{q}(X)\) of compact \(q\)-cycles on a complex reduced analytic space \(X\). Thus, they give a sufficient condition for \(X\) to have only finitely many irreducible compact \(q\)-cycles. Also, they discuss the convexity properties of \(\mathcal{C}_{q}(X)\) by finding conditions under which this space is \(r\)-complete with corners. They perform a very interesting study of convexity properties both in the case where \(q\) is the maximal dimension of a compact irreducible analytic subset of \(X\) and in a situation where \(q\)-cycles are not necessarily maximal.