{"paper":{"title":"Hecke curves and Hitchin discriminant","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jun-Muk Hwang, S. Ramanan","submitted_at":"2003-09-03T09:48:36Z","abstract_excerpt":"Let $C$ be a smooth projective curve of genus $g\\geq 4$ over the complex numbers and ${\\cal SU}^s_C(r,d)$ be the moduli space of stable vector bundles of rank $r$ with a fixed determinant of degree $d$. In the projectivized cotangent space at a general point $E$ of ${\\cal SU}^s_C(r,d)$, there exists a distinguished hypersurface ${\\cal S}_E$ consisting of cotangent vectors with singular spectral curves. In the projectivized tangent space at $E$, there exists a distinguished subvariety ${\\cal C}_E$ consisting of vectors tangent to Hecke curves in ${\\cal SU}^s_C(r,d)$ through $E$. Our main result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309056","kind":"arxiv","version":2},"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"}