{"paper":{"title":"Poincar\\'e polynomials of moduli spaces of one-dimensional sheaves on the projective plane","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Longting Wu, Shuai Guo, with an appendix by Miguel Moreira","submitted_at":"2025-01-09T23:42:10Z","abstract_excerpt":"Let $M_{\\beta}$ denote the moduli space of stable one-dimensional sheaves on a del Pezzo surface $S$, supported on curves of class $\\beta$ with Euler characteristic one. We show that the divisibility property of the Poincar\\'e polynomial of $M_{\\beta}$, proposed by Choi-van Garrel-Katz-Takahashi follows from Bousseau's conjectural refined sheaves/Gromov-Witten correspondence. Since this correspondence is known for $S=\\mathbb{P}^2$, our result proves Choi-van Garrel-Katz-Takahashi's conjecture in this case.\n  For $S=\\mathbb{P}^2$, our proof also introduces a novel approach to computing the Poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05622","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/2501.05622/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"}