{"paper":{"title":"The wobbly divisors of the moduli space of rank-$2$ vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Pauly, Sarbeswar Pal","submitted_at":"2018-03-30T02:14:08Z","abstract_excerpt":"Let $X$ be a smooth projective complex curve of genus $g \\geq 2$ and let $\\M_X(2,\\Lambda)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $\\Lambda$. We show that the wobbly locus, i.e., the locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field is a union of divisors $\\Ww_k \\subset \\M_X(2,\\Lambda)$. We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors $\\Ww_k$ in the Picard group of $\\M_X(2,\\Lambda)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11315","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"}