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Its branch locus ${\\mathcal B}_{0,[n+1]}$ consists of the isomorphism classes of those $(n+1)$-marked spheres with non-trivial group of conformal automorphisms. We prove that ${\\mathcal B}_{0,[n+1]}$ is connected if either $n \\geq 4$ is even or if $n \\geq 6$ is divisible by $3$, and that it has exactly two connected components otherwise. The orbifold ${\\mathcal M}_{0,[n+1]}$ also admits a natural real structure, this being induced by the comple"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.01982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-03T12:51:16Z","cross_cats_sorted":[],"title_canon_sha256":"beae3fe2d0067b6304084894f0ae239dcd5589b95c8283d5e68e76f0f23a6c87","abstract_canon_sha256":"4f9d3467f200c57d70662ede4a1b947bd025e19f979773f093bdc3faebf52aea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:44.963544Z","signature_b64":"y7QaT2YifgXgKkNnPgXhuMVFSFZKMSGoUQ0iPo5r94ouY1r7wdbUmOo8Va9WM0+Z1KPJsSffPPJby5uEshgIBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"612eb9be84c9d7b4f3e0d917a8f10c1728bb323a5ccdc3cfa958f83db1c8cdfe","last_reissued_at":"2026-05-17T23:48:44.963044Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:44.963044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the connectivity of the branch and real locus of ${\\mathcal M}_{0,[n+1]}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rub\\'en A. Hidalgo, Yasmina Atarihuana","submitted_at":"2019-04-03T12:51:16Z","abstract_excerpt":"If $n \\geq 3$, then moduli space ${\\mathcal M}_{0,[n+1]}$, of isomorphisms classes of $(n+1)$-marked spheres, is a complex orbifold of dimension $n-2$. Its branch locus ${\\mathcal B}_{0,[n+1]}$ consists of the isomorphism classes of those $(n+1)$-marked spheres with non-trivial group of conformal automorphisms. We prove that ${\\mathcal B}_{0,[n+1]}$ is connected if either $n \\geq 4$ is even or if $n \\geq 6$ is divisible by $3$, and that it has exactly two connected components otherwise. 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