{"paper":{"title":"The congruence subgroup property for the hyperelliptic modular group: the open surface case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Marco Boggi","submitted_at":"2008-03-27T00:18:45Z","abstract_excerpt":"Let ${\\cal M}_{g,n}$ and ${\\cal H}_{g,n}$, for $2g-2+n>0$, be, respectively, the moduli stack of $n$-pointed, genus $g$ smooth curves and its closed substack consisting of hyperelliptic curves. Their topological fundamental groups can be identified, respectively, with $\\Gamma_{g,n}$ and $H_{g,n}$, the so called Teichm{\\\"u}ller modular group and hyperelliptic modular group. A choice of base point on ${\\cal H}_{g,n}$ defines a monomorphism $H_{g,n}\\hookrightarrow\\Gamma_{g,n}$.\n  Let $S_{g,n}$ be a compact Riemann surface of genus $g$ with $n$ points removed. The Teichm\\\"uller group $\\Gamma_{g,n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3841","kind":"arxiv","version":6},"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"}