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In (https://www.sciencedirect.com/science/article/pii/002240499390049Y) it is mentioned the real section of the moduli space of Riemann surfaces of genus 0. It can be intuitively defined as a subset where the punctures are forced to be on a circle on the sphere.

I guess that one can define a real section by representing the most general punctured sphere $X$ as a two-sheeted cover of the sphere so that we have an involution and we can say that the real section is the set stable under this involution. This should hold at genus one as well

My question is, how can the real section (or "a real section") be defined precisely? Does this definition holds beyond genera 0 and 1?

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  • $\begingroup$ Set of surfaces fixed by $z\to \overline{z}?$ $\endgroup$
    – Igor Rivin
    Commented Mar 9, 2018 at 18:20

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