A new spin on Hurwitz theory and ELSV via theta characteristics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911922766479360 |
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| author | Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo |
| author_facet | Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05697 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A new spin on Hurwitz theory and ELSV via theta characteristics Giacchetto, Alessandro Kramer, Reinier Lewański, Danilo Mathematical Physics Algebraic Geometry Differential Geometry Representation Theory 14N10, 14H10, 05A15, 14N35, 81R10, 05E10, 20C35 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. |
| title | A new spin on Hurwitz theory and ELSV via theta characteristics |
| topic | Mathematical Physics Algebraic Geometry Differential Geometry Representation Theory 14N10, 14H10, 05A15, 14N35, 81R10, 05E10, 20C35 |
| url | https://arxiv.org/abs/2104.05697 |