{"paper":{"title":"The structure of the cohomology ring of the filt schemes","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Takuro Mochizuki","submitted_at":"2003-01-17T14:18:53Z","abstract_excerpt":"Let $C$ be a smooth projective curve over the complex number field $\\cnum$. We investigate the structure of the cohomology ring of the quot schemes $\\Quot(r,n)$, i.e., the moduli scheme of the quotient sheaves of $\\nbigo_C^{\\oplus r}$ with length $n$. We obtain a filtration on $H^{\\ast}(\\Quot(r,n))$, whose associated graded ring has a quite simple structure. As a corollary, we obtain a small generator of the ring. We also obtain a precise combinatorial description of $H^{\\ast}(\\Quot(r,n))$ itself.\n  For that purpose, we consider the complete filt schemes and we use a `splitting principle'. A c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301184","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/math/0301184/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"}