Hilbert Series for Configuration Spaces of Punctured Surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913939722338304 |
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| author | Huang, Yifeng Ramos, Eric |
| author_facet | Huang, Yifeng Ramos, Eric |
| contents | Let $Σ_{g,r}$ denote the $r$-punctured closed Riemann surface of genus $g$. For every $g\geq 0$, we determine the four-variable generating function for the mixed Hodge numbers of the unordered configuration spaces of $Σ_{g,1}$. The cases where $g\geq 2$ are new. Combining a result of \cite{huang2020cohomology}, this determines the analogous generating function for $Σ_{g,r}$ for all $r\geq 1$. As an application of our formula we illustrate how classical homological stability results, as well as so-called secondary stability results of \cite{miller2019higher} can be interpolated to illustrate stable behaviors in the mixed Hodge numbers of these spaces which have been thus-far undiscovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hilbert Series for Configuration Spaces of Punctured Surfaces Huang, Yifeng Ramos, Eric Algebraic Geometry Algebraic Topology Combinatorics Let $Σ_{g,r}$ denote the $r$-punctured closed Riemann surface of genus $g$. For every $g\geq 0$, we determine the four-variable generating function for the mixed Hodge numbers of the unordered configuration spaces of $Σ_{g,1}$. The cases where $g\geq 2$ are new. Combining a result of \cite{huang2020cohomology}, this determines the analogous generating function for $Σ_{g,r}$ for all $r\geq 1$. As an application of our formula we illustrate how classical homological stability results, as well as so-called secondary stability results of \cite{miller2019higher} can be interpolated to illustrate stable behaviors in the mixed Hodge numbers of these spaces which have been thus-far undiscovered. |
| title | Hilbert Series for Configuration Spaces of Punctured Surfaces |
| topic | Algebraic Geometry Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2507.09746 |