{"paper":{"title":"Automorphisms of the Quot schemes associated to compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas, Jacques Hurtubise","submitted_at":"2012-11-14T14:04:03Z","abstract_excerpt":"Let X be a compact connected Riemann surface of genus at least two. Fix positive integers r and d. Let Q denote the Quot scheme that parametrizes the torsion quotients of {\\mathcal O}^{\\oplus r}_X of degree d. This Q is also the moduli space of vortices for the standard action of U(r) on {\\mathbb C}^r. The group \\text{PGL}(r, {\\mathbb C}) acts on Q via the action of $\\text{GL}(r, {\\mathbb C})$ on ${\\mathcal O}^{\\oplus r}_X$. We prove that this subgroup $\\text{PGL}(r, {\\mathbb C})$ is the connected component, containing the identity element, of the holomorphic automorphism group Aut(\\mathcal Q)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3306","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"}