Finite Group Reduction of the DR/DZ Hierarchies

Si-Qi Liu; Youjin Zhang; Tianwen Zhong

Finite Group Reduction of the DR/DZ Hierarchies

Algebraic Geometry 2026-07-18 v1

Authors: Si-Qi Liu , Youjin Zhang , Tianwen Zhong

Abstract

We show that the finite group reduction of the Dubrovin-Zhang/Double Ramification hierarchy associated to a semisimple CohFT preserves its bihamiltonian structure and its tau structure. By applying this result to the orbifold Gromov-Witten theory with the target $\mathbb{P}^1_{2,2,2,2}$ , we see that there are two different and interesting integrable hierarchies that can be associated to the Frobenius manifold structure on the Hurwitz space $M_{1;1}$ . One of them is equivalent to the genus $1$ topological recursion.

Keywords

finite group reduction DR/DZ hierarchies bihamiltonian structure tau structure Gromov-Witten theory

Cite

@article{arxiv.2607.16607,
  title  = {Finite Group Reduction of the DR/DZ Hierarchies},
  author = {Si-Qi Liu and Youjin Zhang and Tianwen Zhong},
  journal= {arXiv preprint arXiv:2607.16607},
  year   = {2026}
}