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Abstract

We describe a supersymmetric generalization of the construction of Kontsevich
and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between
the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our
main result is the existence of a flat holomorphic connection on the line
bundle $\lambda_{3/2}\otimes\lambda_{1/2}^{-5}$ on the moduli space of triples:
a super Riemann surface, a Neveu-Schwarz puncture, and a formal coordinate
system. We also prove a superconformal Noether normalization lemma for families
of super Riemann surfaces.