{"paper":{"title":"On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"L. Brambila-Paz, O. Mata-Guti\\'errez","submitted_at":"2012-08-03T23:51:38Z","abstract_excerpt":"Let $M(n,\\xi)$ be the moduli space of stable vector bundles of rank $n\\geq 3$ and fixed determinant $\\xi$ over a smooth projective algebraic curve $X$ over $\\mathbb{C}$ of genus $g\\geq 4.$ We use the gonality of the curve and $r$-Hecke morphisms to describe a smooth open set and to compute the dimension of a component of the Hilbert scheme $Hilb_{M(n,\\xi)}$, of the scheme of morphisms $Mor(\\mathbb{G},M(n,\\xi))$ and of the moduli space $ M_{X \\times \\mathbb{G}}$ of stable bundles over $X\\times \\mathbb{G},$ where $\\mathbb{G}$ is the Grassmannian $\\mathbb{G}(n-r,\\mathbb{C}^n)$. In particular, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0869","kind":"arxiv","version":3},"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"}