On super curves and supervolumes
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911775589400576 |
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| author | Castillo, Ricardo Jesús Ramos |
| author_facet | Castillo, Ricardo Jesús Ramos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On super curves and supervolumes Castillo, Ricardo Jesús Ramos Representation Theory 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. |
| title | On super curves and supervolumes |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2402.07815 |