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arXiv · 2002.06625

The Super Mumford Form and Sato Grassmannian

Katherine A. Maxwell
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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.

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BibTeXRIS

Katherine A. Maxwell. 2020-02-16. The Super Mumford Form and Sato Grassmannian. https://doi.org/10.1016/j.geomphys.2022.104604

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