{"paper":{"title":"Hilbert Series for Configuration Spaces of Punctured Surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.AG","authors_text":"Eric Ramos, Yifeng Huang","submitted_at":"2025-07-13T18:56:06Z","abstract_excerpt":"Let $\\Sigma_{g,r}$ 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 $\\Sigma_{g,1}$. The cases where $g\\geq 2$ are new. Combining a result of \\cite{huang2020cohomology}, this determines the analogous generating function for $\\Sigma_{g,r}$ 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 t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09746","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.09746/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}