• 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…

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## References

SHOWING 1-10 OF 66 REFERENCES
A new cohomology class on the moduli space of curves
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
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
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
Journal 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
• 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
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
JT gravity as a matrix integral
• Mathematics
• 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
On the tautological ring of Mg,n
In this section, we briefly describe the objects under consideration for the sake of non-experts. A more detailed informal exposition of these well-known ideas is given in [PV]. When studying Riemann