On the structure of Goulden-Jackson-Vakil formula

We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural “intersection numbers” on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the properly arranged generating function for these “intersection numbers”, and prove that it satisfies Hirota equations. This generalizes and substantially simplifies our earlier results with Zvonkine.

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Published 1 January 2009