Super quantum cohomology I: Super stable maps of genus zero with Neveu-Schwarz punctures

In this article we define stable supercurves and super stable maps of genus zero via labeled trees. We prove that the moduli space of stable supercurves and super stable maps of fixed tree type are quotient superorbifolds. To this end, we prove a slice theorem for the action of super Lie groups on supermanifolds with finite isotropy groups and discuss superorbifolds. Furthermore, we propose a generalization of Gromov convergence to super stable maps such that the restriction to fixed tree type yields the quotient topology from the superorbifold and the reduction is compact. This would, possibly, lead to the notions of super Gromov-Witten invariants and small super quantum cohomology to be discussed in sequels.