Mathematical Research Letters

Volume 16 (2009)

Number 4

On the structure of Goulden-Jackson-Vakil formula

Pages: 703 – 710

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n4.a11

Author

S. Shadrin (University of Amsterdam)

Abstract

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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