{"paper":{"title":"Rational curves and lines on the moduli space of stable bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mingshuo Zhou","submitted_at":"2013-05-15T09:06:33Z","abstract_excerpt":"Fix a smooth projetive curve $\\mathcal {C}$ of genus $g\\geq 2$ and a line bundle $\\mathcal{L}$ on $\\mathcal{C}$ of degree $d$. Let $M:= \\mathcal{SU}_{\\mathcal{C}}(r, \\mathcal{L})$ be the moduli space of stable vector bundles on $\\mathcal{C}$ of rank $r$ and with fixed determinant $\\mathcal{L}$. We prove that any rational curve on $M$ is a generalized Hecke curve. Furthermore, we study the lines on $M$, and prove that $M$ is covered by the lines when $(r, d)=r$; for the case $(r,d)<r$, the lines fill up a closed subvariety of $M$, and we determine the number of its irreducible components and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3394","kind":"arxiv","version":5},"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"}