See the Kontesevich paper “Enumeration of Rational Curves via Torus Actions.”
Definition
A stable map with target \(X\) is a structure \((C, f, x_1,...,x_n)\) consisting of a connected compact reduced curve \(C\) with \(n\geq 0\) many pairwise distinct non-singular points \(x_i\) and at most ordinary double singularities, and a map \(f:C\to X\) having no non-trivial first order infinitesmal automorphisms, identical on \(V\) and \(x_1,...,x_n\).