Giacchetto, Alessandro and Kramer, Reinier and Lewanski, Danilo (2021) A new spin on Hurwitz theory and ELSV via theta characteristics. MPIM Preprint Series 2021 (14).
Preview |
Text
mpim-preprint_2021-14.pdf - Submitted Version Download (633kB) | Preview |
Abstract
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of Kähler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological recursion. We prove that this conjectural topological recursion is equivalent to an ELSV-type formula, expressing spin Hurwitz numbers in terms of the Chiodo class twisted by the 2-spin Witten class.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 1 Discrete mathematics / algebra > 14-XX Algebraic geometry |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 18 May 2021 09:59 |
| Last Modified: | 18 May 2021 11:04 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4544 |
Actions (login required)
 |
View Item |