{"paper":{"title":"On the stabilization of the Betti numbers of the moduli space of sheaves on $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sayanta Mandal","submitted_at":"2019-08-27T01:30:06Z","abstract_excerpt":"Let $r \\geq 2$ be an integer, and let $a$ be an integer coprime to $r$. We show that if $c_2 \\geq n + \\left\\lfloor \\frac{r-1}{2r}a^2 + \\frac{1}{2}(r^2 + 1) \\right\\rfloor$, then the $2n$th Betti number of the moduli space $M_{\\mathbb{P}^2,H}(r,aH,c_2)$ stabilizes, where $H = c_1(\\mathcal{O}_{\\mathbb{P}^2}(1))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09977","kind":"arxiv","version":2},"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/1908.09977/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"}