Equivariant Hodge polynomials of heavy/light moduli spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910415901949952 |
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| author | Kannan, Siddarth Serpente, Stefano Yun, Claudia He |
| author_facet | Kannan, Siddarth Serpente, Stefano Yun, Claudia He |
| contents | Let $\bar{\mathcal{M}}_{g, m|n}$ denote Hassett's moduli space of weighted pointed stable curves of genus $g$ for the heavy/light weight data $\left(1^{(m)}, 1/n^{(n)}\right)$, and let $\mathcal{M}_{g, m|n} \subset \bar{\mathcal{M}}_{g, m|n}$ be the locus parameterizing smooth, not necessarily distinctly marked curves. We give a change-of-variables formula which computes the generating function for $(S_m\times S_n)$-equivariant Hodge-Deligne polynomials of these spaces in terms of the generating functions for $S_{n}$-equivariant Hodge-Deligne polynomials of $\bar{\mathcal{M}}_{g,n}$ and $\mathcal{M}_{g,n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_02800 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equivariant Hodge polynomials of heavy/light moduli spaces Kannan, Siddarth Serpente, Stefano Yun, Claudia He Algebraic Geometry 14H10 Let $\bar{\mathcal{M}}_{g, m|n}$ denote Hassett's moduli space of weighted pointed stable curves of genus $g$ for the heavy/light weight data $\left(1^{(m)}, 1/n^{(n)}\right)$, and let $\mathcal{M}_{g, m|n} \subset \bar{\mathcal{M}}_{g, m|n}$ be the locus parameterizing smooth, not necessarily distinctly marked curves. We give a change-of-variables formula which computes the generating function for $(S_m\times S_n)$-equivariant Hodge-Deligne polynomials of these spaces in terms of the generating functions for $S_{n}$-equivariant Hodge-Deligne polynomials of $\bar{\mathcal{M}}_{g,n}$ and $\mathcal{M}_{g,n}$. |
| title | Equivariant Hodge polynomials of heavy/light moduli spaces |
| topic | Algebraic Geometry 14H10 |
| url | https://arxiv.org/abs/2207.02800 |