Towards an orbifold generalization of Zvonkine's r-ELSV formula

Kramer, Reinier; Lewanski, Danilo; Popolitov, Alexandr; Shadrin, Sergey

doi:10.1090/tran/7793

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Towards an orbifold generalization of Zvonkine's r-ELSV formula

MPS-Authors

/persons/resource/persons235691

Lewanski, Danilo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1090/tran/7793
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

arXiv:1703.06725.pdf
(Preprint), 291KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Kramer, R., Lewanski, D., Popolitov, A., & Shadrin, S. (2019). Towards an orbifold generalization of Zvonkine's r-ELSV formula. Transactions of the American Mathematical Society, 372(6), 4447-4469. doi:10.1090/tran/7793.

Cite as: https://hdl.handle.net/21.11116/0000-0004-F96E-9

Abstract

We perform a key step towards the proof of Zvonkine's conjectural $r$-ELSV formula that relates Hurwitz numbers with completed $(r+1)$-cycles to the geometry of the moduli spaces of the $r$-spin structures on curves: we prove the quasi-polynomiality property prescribed by Zvonkine's conjecture. Moreover, we propose an orbifold generalization of Zvonkine's conjecture and prove the quasi-polynomiality property in this case as well. In addition to that, we study the $(0,1)$- and $(0,2)$-functions in this generalized case and we show that these unstable cases are correctly reproduced by the spectral curve initial data.