{"paper":{"title":"Moduli of parabolic connections on a curve and Riemann-Hilbert correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michi-aki Inaba","submitted_at":"2006-02-01T01:54:15Z","abstract_excerpt":"Let $(C,\\bt)$ ($\\bt=(t_1,...,t_n)$) be an $n$-pointed smooth projective curve of genus $g$ and take an element $\\blambda=(\\lambda^{(i)}_j)\\in\\C^{nr}$ such that $-\\sum_{i,j}\\lambda^{(i)}_j=d\\in\\mathbf{Z}$. For a weight $\\balpha$, let $M_C^{\\balpha}(\\bt,\\blambda)$ be the moduli space of $\\balpha$-stable $(\\bt,\\blambda)$-parabolic connections on $C$ and let $RP_r(C,\\bt)_{\\ba}$ be the moduli space of representations of the fundamental group $\\pi_1(C\\setminus\\{t_1,...,t_n\\},*)$ with the local monodromy data $\\ba$ for a certain $\\ba\\in\\C^{nr}$. Then we prove that the morphism $\\RH:M_C^{\\balpha}(\\bt,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602004","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"}