Moduli stacks of maps for supermanifolds

Abstract

We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry of supermanifolds to include a treatment of superstacks we prove that such moduli problems, under suitable conditions, give rise to Deligne-Mumford superstacks (where all of these objects have natural definitions in terms of supergeometry). We make some observations about the properties of these moduli superstacks, as well as some remarks about their application in physics and their associated Gromov-Witten theory.