Low degree Hurwitz stacks in the Grothendieck ring
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916993756561408 |
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| author | Landesman, Aaron Vakil, Ravi Wood, Melanie Matchett |
| author_facet | Landesman, Aaron Vakil, Ravi Wood, Melanie Matchett |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_01840 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Low degree Hurwitz stacks in the Grothendieck ring Landesman, Aaron Vakil, Ravi Wood, Melanie Matchett Algebraic Geometry Number Theory 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. |
| title | Low degree Hurwitz stacks in the Grothendieck ring |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2203.01840 |