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We study the geometry of super curves with a chosen supervolume form. We consider the algebra of divergence free vector fields S (1|N) associated to such curves. When N=2 its derived algebra, called S (2), defines a special family of curves, named S (2) -super curves. We exhibit an involution on the moduli space of such curves that generalizes Deligne's involution for N=1 super curves. The fixed point set of this involution consists on Manin's SUSY₂-super curves. We describe the moduli spaces of these curves.
Ricardo Jesús Ramos Castillo (Mon,) studied this question.