{"paper":{"title":"On moduli spaces of Hitchin pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Marina Logares, Peter B. Gothen","submitted_at":"2009-12-23T11:45:23Z","abstract_excerpt":"Let $X$ be a compact Riemann surface $X$ of genus at--least two. Fix a holomorphic line bundle $L$ over $X$. Let $\\mathcal M$ be the moduli space of Hitchin pairs $(E ,\\phi\\in H^0(End(E)\\otimes L))$ over $X$ of rank $r$ and fixed determinant of degree $d$. We prove that, for some numerical conditions, $\\mathcal M$ is irreducible, and that the isomorphism class of the variety $\\mathcal M$ uniquely determines the isomorphism class of the Riemann surface $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4615","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"}