{"paper":{"title":"Infinitesimal deformations of some Quot schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chandranandan Gangopadhyay, Indranil Biswas, Ronnie Sebastian","submitted_at":"2022-03-24T16:10:24Z","abstract_excerpt":"Let $E$ be a vector bundle on a smooth complex projective curve $C$ of genus at least two. Let $\\mathcal{Q}(E,d)$ be the Quot scheme parameterizing the torsion quotients of $E$ of degree $d$. We compute the cohomologies of the tangent bundle $T_{\\mathcal{Q}(E,d)}$. In particular, the space of infinitesimal deformations of $\\mathcal{Q}(E,d)$ is computed. Kempf and Fantechi computed the space of infinitesimal deformations of $\\mathcal{Q}(\\mathcal{O}_C,d)\\,=\\, C^{(d)}$. We also explicitly describe the infinitesimal deformations of $\\mathcal{Q}(E,d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13150","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/2203.13150/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"}