# 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…

## 12 Citations

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

- Physics, MathematicsLetters 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, Physics
- 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…

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

- Mathematics, Physics
- 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, Physics
- 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…

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

- Physics, 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

- 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…

JT supergravity and Brezin-Gross-Witten tau-function

- Physics
- 2020

We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and…

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {N}}=1$$\end{document}N=1 super topological recursion

- MedicineLetters in mathematical physics
- 2021

The notion of the minimal super loop equations is introduced and can be applied to compute correlation functions for a variety of examples related to 2d supergravity.

## References

SHOWING 1-10 OF 66 REFERENCES

A new cohomology class on the moduli space of curves

- Mathematics, Physics
- 2017

We define a collection of cohomology classes $\Theta_{g,n}\in H^{4g-4+2n}(\overline{\cal M}_{g,n})$ for $2g-2+n>0$ that restrict naturally to boundary divisors. We prove that a generating function…

Gromov-Witten invariants of $\mathbb{P}^1$ coupled to a KdV tau function

- Mathematics, Physics
- 2018

We consider the pull-back of a natural sequence of cohomology classes $\Theta_{g,n}\in H^{2(2g-2+n)}(\overline{\cal M}_{g,n})$ to the moduli space of stable maps ${\cal M}^g_n(\mathbb{P}^1,d)$. These…

Invariants of spectral curves and intersection theory of moduli spaces of complex curves

- Mathematics, Physics
- 2011

To any spectral curve S, we associate a topological class {\Lambda}(S) in a moduli space M^b_{g,n} of "b-colored" stable Riemann surfaces of given topology (genus g, n boundaries), whose integral…

Decorated super-Teichmüller space

- Mathematics, PhysicsJournal of Differential Geometry
- 2019

We introduce coordinates for a principal bundle $S\tilde T(F)$ over the super Teichmueller space $ST(F)$ of a surface $F$ with $s\geq 1$ punctures that extend the lambda length coordinates on the…

Topological recursion on the Bessel curve

- Mathematics, Physics
- 2016

The Witten-Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This…

Towards an Enumerative Geometry of the Moduli Space of Curves

- Mathematics
- 1983

The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli…

Weil-Petersson volumes and intersection theory on the moduli space of curves

- Mathematics
- 2006

In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,…

JT gravity as a matrix integral

- Physics
- 2019

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the…

Moduli of vector bundles on curves with parabolic structures

- Mathematics
- 1980

Let H be the upper half plane and T a discrete subgroup of AutH. Suppose that H mod Y is of finite measure. This work stems from the question whether there is an algebraic interpretation for the…

Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points

- Mathematics
- 1992

In [9], A. Floer considered the Chern-Simons functional on the space of connexions on a homology 3-sphere C and, using Morse theoretic methods, defined periodic homology groups HZ,(C). The Euler…