Enumerative geometry via the moduli space of super Riemann surfaces [article]

Paul Norbury
2020 arXiv   pre-print
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces M_g,n. This allows us to use a recursion between the super volumes recently proven by Stanford and Witten to deduce recursion relations of a natural collection of cohomology classes Θ_g,n∈ H^*( M_g,n). We give a new proof that a generating function for the intersection numbers of Θ_g,n with tautological classes on M_g,n is a KdV tau function. This is an
more » ... e of the Kontsevich-Witten theorem where Θ_g,n is replaced by the unit class 1∈ H^*( M_g,n). The proof is analogous to Mirzakhani's proof of the Kontsevich-Witten theorem replacing volumes of moduli spaces of hyperbolic surfaces with volumes of moduli spaces of super hyperbolic surfaces.
arXiv:2005.04378v1 fatcat:5ve7sc5ubvfdxignocqakjapoq