{"paper":{"title":"Moduli spaces of witch curves topologically realize the 2-associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Nathaniel Bottman","submitted_at":"2017-12-04T16:57:53Z","abstract_excerpt":"For $r \\geq 1$ and $\\mathbf{n} \\in \\mathbb{Z}_{\\geq0}^r\\setminus\\{\\mathbf{0}\\}$, we construct the compactified moduli space $\\overline{2\\mathcal{M}}_{\\mathbf{n}}$ of witch curves of type $\\mathbf{n}$. We equip $\\overline{2\\mathcal{M}}_{\\mathbf{n}}$ with a stratification by the 2-associahedron $W_{\\mathbf{n}}$, and prove that $\\overline{2\\mathcal{M}}_{\\mathbf{n}}$ is compact and metrizable. In addition, we show that the forgetful map $\\overline{2\\mathcal{M}}_{\\mathbf{n}} \\to \\overline{\\mathcal{M}}_r$ to the moduli space of stable disk trees is continuous and respects the stratifications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01194","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1712.01194/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}