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arXiv · 2402.07815

On super curves and supervolumes

Ricardo Jesús Ramos Castillo
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Abstract

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 $SUSY_2$-super curves. We describe the moduli spaces of these curves.

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Ricardo Jesús Ramos Castillo. 2024-02-12. On super curves and supervolumes. https://arxiv.org/abs/2402.07815

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