• Corpus ID: 218581376

Enumerative geometry via the moduli space of super Riemann surfaces

@article{Norbury2020EnumerativeGV,
  title={Enumerative geometry via the moduli space of super Riemann surfaces},
  author={Paul T. Norbury},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}

• P. Norbury
• Published 9 May 2020
• Mathematics
• arXiv: Algebraic Geometry

In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. 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 $\Theta_{g,n}\in H^*(\overline{\cal M}_{g,n})$. We give a new proof that a generating function for the intersection numbers of $\Theta_{g,n}$ with tautological classes on $\overline{\cal M}_{g,n}$ is a KdV tau function. This is an analogue of the Kontsevich-Witten theorem where $\Theta_{g,n}$ is replaced by the unit class $1\in H^*(\overline{\cal M}_{g,n})$. 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.