The Hodge-FVH Correspondence
Si-Qi Liu, Di Yang, Youjin Zhang, Chunhui Zhou
TL;DR
This paper proves the Hodge-FVH correspondence linking special cubic Hodge integrals to the fractional Volterra hierarchy, and applies it to establish a gap condition and an algorithm for coefficient computation.
Contribution
It establishes the proof of the Hodge-FVH correspondence and introduces an algorithm for computing coefficients in the gap condition.
Findings
Proof of the Hodge-FVH correspondence.
Establishment of a gap condition for specific cubic Hodge integrals.
Development of an algorithm for coefficient calculation.
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Polynomial and algebraic computation