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The Hodge-FVH correspondence

  • Si-Qi Liu , Di Yang EMAIL logo , Youjin Zhang and Chunhui Zhou


The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application of this result, we prove a gap condition for certain special cubic Hodge integrals and give an algorithm for computing the coefficients that appear in the gap condition.

Award Identifier / Grant number: 11771238

Award Identifier / Grant number: 11725104

Award Identifier / Grant number: 11671371

Funding statement: This work is partially supported by NSFC No. 11771238, No. 11725104, No. 11671371. Part of the work of Chunhui Zhou was done during his PhD studies at Tsinghua University; he thanks Tsinghua University for excellent working conditions and financial supports.


We are grateful to Boris Dubrovin for his support of the work and very helpful discussions. We would like to thank Shuai Guo, Yongbin Ruan and Don Zagier for their interests and helpful comments.


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Received: 2019-10-07
Revised: 2020-12-10
Published Online: 2021-02-23
Published in Print: 2021-06-01

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