{"paper":{"title":"An observation on the Poincar\\'e polynomials of moduli spaces of one-dimensional sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Oleksandr Iena","submitted_at":"2018-05-07T16:49:06Z","abstract_excerpt":"We notice that for $0<d\\le 6$ the Poincar\\'e polynomial of Simpson moduli space $M_{dm + 1}(\\mathbb P_2)$ is divisible by the Poincar\\'e polynomial of the projective space $\\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of the Poincar\\'e polynomials of the Hilbert scheme of $\\frac{(d-2)(d-1)}{2}$ points on $\\mathbb P_2$ and the moduli space of Kronecker modules $N(3; d-2, d-1)$ is noticed for $d=4, 5, 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02616","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":""},"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"}