In this companion piece to [9], some variations on the main results there are sketched. In particular,
• the recursions in [9], which we interpreted as the quantum Lefschetz, is re- formulated in terms of Givental’s quantization formalism, or equivalently, a summation of finitely many graphs;
• varietiesofmodificationoftheauxilliaryspaces(masterspaces)forthefixed point localization are given, leading to different (looking) recursions;
• applications of this circle of ideas to derive (apparently) new relations of Gromov–Witten invariants.