{"paper":{"title":"A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yashonidhi Pandey","submitted_at":"2013-04-12T16:55:29Z","abstract_excerpt":"Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \\mathrm{Sym}^2(V) \\ra \\mathcal{O}_X$ (respectively symplectic form $q: \\Lambda^2V \\ra \\mathcal{O}_X$). Fixing the degeneracy locus of the quadratic form induced on $V/\\ker(q)$, we construct a coarse moduli of such objects. Further, we prove semi-stable reduction theorem for equivalence classes of such objects. In particular, the case when degeneracies of $q$ are higher than one is that of principal interest. We also provide a proof of properness of polystable orthogonal bundles without appealing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3682","kind":"arxiv","version":4},"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"}