The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908955334148096 |
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| author | Landi, Alberto |
| author_facet | Landi, Alberto |
| contents | We study the integral Chow ring of the stack $\mathcal{H}_{g,n}$ parametrizing $n$-pointed smooth hyperelliptic curves of genus $g$. We compute the integral Chow ring of $\mathcal{H}_{g,n}$ for $n=1,2$ completely, while for $3\leq n\leq2g+2$ we compute it up to the additive order of a single class in degree 2. We obtain partial results also for $n=2g+3$. In particular, taking $g=2$ and recalling that $\mathcal{H}_{2,n}=\mathcal{M}_{2,n}$, our results hold for $\mathrm{CH}^*(\mathcal{M}_{2,n})$ for $1\leq n\leq7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves Landi, Alberto Algebraic Geometry 14C15 (primary), 14D23, 14H10 (secondary) We study the integral Chow ring of the stack $\mathcal{H}_{g,n}$ parametrizing $n$-pointed smooth hyperelliptic curves of genus $g$. We compute the integral Chow ring of $\mathcal{H}_{g,n}$ for $n=1,2$ completely, while for $3\leq n\leq2g+2$ we compute it up to the additive order of a single class in degree 2. We obtain partial results also for $n=2g+3$. In particular, taking $g=2$ and recalling that $\mathcal{H}_{2,n}=\mathcal{M}_{2,n}$, our results hold for $\mathrm{CH}^*(\mathcal{M}_{2,n})$ for $1\leq n\leq7$. |
| title | The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves |
| topic | Algebraic Geometry 14C15 (primary), 14D23, 14H10 (secondary) |
| url | https://arxiv.org/abs/2404.15873 |