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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 $\\M_X(2,\\Lambda)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.11315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-30T02:14:08Z","cross_cats_sorted":[],"title_canon_sha256":"d377de8f0bcab42582d2d7ceadab3c497454773b2ef4998fb2eef4d0567e584e","abstract_canon_sha256":"0db183420a868460262da6d96a7c240e0b4bbb3249eac0d86f25efd481b9a2a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:44.060910Z","signature_b64":"30ZsucDfHIEo9CxtbWkNXriK8+L92rXtIKGjEiLVq+v5vqk8G3U72a2fUiAgC7bwGTAiDAA/RSZxmLLYRZVsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf78c0182abaa57eab7dd07adc091e5cc939c2da968dfb25e0299a4973285d85","last_reissued_at":"2026-05-18T00:19:44.060208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:44.060208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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