The Hodge-FVH Correspondence

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.

Added Proposition 1.2 and Theorem 1.3; added references; corrected typos; 43 pages