# Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality

@inproceedings{Dubrovin2021GeometryAA, title={Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality}, author={Boris Dubrovin and Di Yang and Don Zagier}, year={2021} }

For each of the simple Lie algebras g = Al, Dl or E6, we show that the all-genera one-point FJRW invariants of g-type, after multiplication by suitable products of Pochhammer symbols, are the coefficients of an algebraic generating function and hence are integral. Moreover, we find that the all-genera invariants themselves coincide with the coefficients of the unique calibration of the Frobenius manifold of g-type evaluated at a special point. For the A4 (5-spin) case we also find two other…

## 4 Citations

### On tau-functions for the KdV hierarchy

- MathematicsSelecta Mathematica
- 2021

For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic…

### On the large genus asymptotics of psi-class intersection numbers

- MathematicsMathematische Annalen
- 2022

Based on an explicit formula of the generating series for the n-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [10]…

### Punctures and p-Spin Curves from Matrix Models II

- Materials ScienceJournal of Statistical Physics
- 2021

We report here an extension of a previous work in which we have shown that matrix models provide a tool to compute the intersection numbers of p-spin curves. We discuss further an extension to…

### Punctures and p-Spin Curves from Matrix Models III. Dl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_l$$\end{docume

- Materials ScienceJournal of Statistical Physics
- 2022

The intersection numbers for p spin curves of the moduli space M¯g,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

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