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Low-degree Hurwitz stacks in the Grothendieck ring
Published online by Cambridge University Press: 11 September 2024
Abstract
For 
$2 \leq d \leq 5$, we show that the class of the Hurwitz space of smooth degree 
$d$, genus 
$g$ covers of 
$\mathbb {P}^1$ stabilizes in the Grothendieck ring of stacks as 
$g \to \infty$, and we give a formula for the limit. We also verify this stabilization when one imposes ramification conditions on the covers, and obtain a particularly simple answer for this limit when one restricts to simply branched covers.
MSC classification
- Type
- Research Article
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- Copyright
- © 2024 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
Footnotes
With an appendix by Aaron Landesman and Federico Scavia
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