{"paper":{"title":"A stratification of the moduli space of vector bundles on curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"H. Lange, L. Brambila-Paz","submitted_at":"1997-08-18T07:52:26Z","abstract_excerpt":"Let $E$ be a vector bundle of rank $r\\geq 2$ on a smooth projective curve $C$ of genus $g \\geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\\le k\\le r-1$ we define $${\\se}_k(E):=k\\deg E-r\\max\\deg F.$$ where the maximum is taken over all subbundles $F$ of rank $k$ of $E$. The ${s}_k$ gives a stratification of the moduli space ${\\cal M}(r,d)$ of stable vector bundles of rank $r$ and degree on $d$ on $C$ into locally closed subsets ${\\calM}(r,d,k,s)$ according to the value of $s$ and $k$. There is a component ${\\cal M}^0(r,d,k,s)$ of ${\\cal M}(r,d,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708014","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"}