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Tropical spin Hurwitz numbers
Abstract
We introduce a tropical framework for the study of spin Hurwitz numbers and their completed cycles analogues. We use degeneration techniques to obtain an interpretation of spin Hurwitz numbers via tropical covers. We employ the tropical methods to obtain new closed formulae for spin Hurwitz numbers in special cases. Moreover, we employ Fock space techniques to tropicalise completed cycles spin Hurwitz numbers. Using this, we prove that spin Hurwitz numbers admit a piecewise polynomial structure akin to their classical counterparts. We also derive wall--crossing formulae.
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BibTeX
@misc{cobigo2026tropical,
title = {{Tropical spin Hurwitz numbers}},
author = {Lou-Jean Leila Cobigo and Marvin Anas Hahn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36390},
eprint = {2610.36390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36390},
}
RIS
TY - UNPB
TI - Tropical spin Hurwitz numbers
AU - Lou-Jean Leila Cobigo
AU - Marvin Anas Hahn
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36390
UR - https://arxiv.org/abs/2610.36390
AB - We introduce a tropical framework for the study of spin Hurwitz numbers and their completed cycles analogues. We use degeneration techniques to obtain an interpretation of spin Hurwitz numbers via tropical covers. We employ the tropical methods to obtain new closed formulae for spin Hurwitz numbers in special cases. Moreover, we employ Fock space techniques to tropicalise completed cycles spin Hurwitz numbers. Using this, we prove that spin Hurwitz numbers admit a piecewise polynomial structure akin to their classical counterparts. We also derive wall--crossing formulae.
ER -