English

On the structure of Goulden-Jackson-Vakil formula

Algebraic Geometry 2018-07-18 v1 Combinatorics

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 Xg,nX_{g,n} of dimension 4g3+n4g-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 in arXiv:math/0602457.

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Cite

@article{arxiv.0810.0729,
  title  = {On the structure of Goulden-Jackson-Vakil formula},
  author = {S. Shadrin},
  journal= {arXiv preprint arXiv:0810.0729},
  year   = {2018}
}

Comments

9 pages

R2 v1 2026-06-21T11:27:17.098Z