A super Riemann surface $M$ is a complex supermanifold of dimension 1|1 with a superconformal structure given locally by an odd vector field $D=\frac{\partial}{\partial\theta}+\theta\frac{\partial}{\partial z}$. My question is, what are the right notions of (super) holomorphic and meromorphic funtions on $M$, and also the notion of a divisor on $M$? Finally, is it known if the classical theorems (Hurwitz formula, Serre duality, Riemann–Roch, "if $M$ is compact any line bundle is the bundle of a divisor", etc) hold for super Riemann surfaces?

I also appreciate if someone could give some good references for these topics.

Thank you in advance.

  • $\begingroup$ Hi, a good starting point might be "Geometry of superconformal manifolds" by Rosly, Schwarz and Voronov. $\endgroup$ – ruediger Oct 29 '15 at 16:19

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