# 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} }

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…

## 16 Citations

$${\mathcal {N}}=1$$ super topological recursion

- PhysicsLetters in Mathematical Physics
- 2021

We introduce the notion of $${\mathcal {N}}=1$$
N
=
1
abstract super loop equations and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be…

Cut-and-join operators for higher Weil-Petersson volumes

- Mathematics
- 2021

In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of ψ, κ, and Θ classes on the moduli spaces Mg,n. The cut-and-join operators…

Polynomial relations among kappa classes on the moduli space of curves

- Mathematics
- 2021

We construct an infinite collection of universal—independent of (g, n)—polynomials in the Miller-Morita-Mumford classes κm ∈ H(Mg,n,Q), defined over the moduli space of genus g stable curves with n…

Higher Br\'ezin-Gross-Witten tau-functions and intersection theory of Witten's and Norbury's classes

- Mathematics
- 2022

. In this paper, we consider the higher Br´ezin–Gross–Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac–Schwarz operators, quantum spectral…

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

- Mathematics
- 2021

In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi–Yau condition. For the tau-functions, which generate these integrals, we derive the complete families…

A Simple Recursion for the Mirzakhani Volume and its Super Extension

- Mathematics
- 2020

In this paper, we derived a simple recursion formula for the volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula reflects clearly that the volumes are polynomials. By…

A Simple Recursion for the Mirzakhani Volume and its Supersymmetric Extension

- Mathematics
- 2020

In this paper, we derived a simple recursion formula for the volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula reflects clearly that the volumes are polynomials. By…

Cut-and-join operators in cohomological field theory and topological recursion

- Mathematics
- 2022

We construct a cubic cut-and-join operator description for the partition function of the Chekhov–Eynard–Orantin topological recursion for a local spectral curve with simple ramification points. In…

Generalized Br\'ezin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy

- Mathematics
- 2021

In this paper, we prove that the generalized Brézin–Gross–Witten taufunction is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim that it describes a…

D ec 2 02 0 Intersection numbers on M g , n and BKP hierarchy

- Mathematics
- 2020

In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich–Witten tau-function in terms of the Schur Q-functions. Here we provide a similar…

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