Mathematical Research Letters
Volume 16, Issue 4, July 2009 pp. 703-710.
On the structure of Goulden-Jackson-Vakil formulaAuthors: S. Shadrin
Author institution: University of Amsterdam
Summary: 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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