Abstract
We give a summary of some elementary results in the theory of super Rie-mann surfaces (SUSY curves), which are mostly known, but are not readily available in the literature. In particular, we give the classification of all genus 0 SUSY-1 curves and touch on the case of genus 1. We also briefly discuss the related topic of П-projective spaces.
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Notes
- 1.
1 We may denote the linear superspace ℂ⊕m ⊕ (П ℂ)⊕n simply with ℂm|n whenever it is clear it is not the complex supermanifold introduced at the beginning of this section.
- 2.
2 All of our arguments here take place for an open cover of T in which a T point corresponds to a free sheaf and not just a locally free one. For simplicity of exposition we omit to mention the cover and the necessary gluing to make all of our argument stand.
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Fioresi, R., Kwok, S.D. (2014). On SUSY curves. In: Gorelik, M., Papi, P. (eds) Advances in Lie Superalgebras. Springer INdAM Series, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02952-8_7
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DOI: https://doi.org/10.1007/978-3-319-02952-8_7
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