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We prove that if either $n\\neq 2$ or $\\dim(X)\\geq 2$, then the connected component of the identity of $Aut(X[n])$ is isomorphic to the connected component of the identity of $Aut(X)$. When $X = C$ is a curve of genus $g(C)\\neq 1$ we classify the dominant morphisms $C[n]\\rightarrow C[r]$, and thanks to this we manage to compute the whole automorphism group of $C[n]$, namely $Aut(C[n])\\cong S_n\\times Aut(C)$ for any $n\\neq 2$, while $Aut(C[2])\\cong S_2\\ltimes "},"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":"1603.06991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-22T21:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"9b2b6d73b10b964d628540d8ccc79d420d75db74da3f5393796d84d1d94063c2","abstract_canon_sha256":"5be2af176a3271105e35c6c6a54ce975807e0c488527fcb3b507b70635c77e57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:02.508026Z","signature_b64":"443H0JnibPq+NCo14S6seG5CpP8l+bkUH9MyK7FQeYM7kR3U9On0D1wCjTBhPYHw8f0kEaOIOiIViNkXehQLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c07e782c70fa6fbdbf15761cb30e65bb1943205a0af10b77d9ebfaf16c40e30b","last_reissued_at":"2026-05-18T00:33:02.507479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:02.507479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the biregular geometry of the Fulton-MacPherson compactification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Massarenti","submitted_at":"2016-03-22T21:27:03Z","abstract_excerpt":"Let $X[n]$ be the Fulton-MacPherson compactification of the configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\\neq 2$ or $\\dim(X)\\geq 2$, then the connected component of the identity of $Aut(X[n])$ is isomorphic to the connected component of the identity of $Aut(X)$. When $X = C$ is a curve of genus $g(C)\\neq 1$ we classify the dominant morphisms $C[n]\\rightarrow C[r]$, and thanks to this we manage to compute the whole automorphism group of $C[n]$, namely $Aut(C[n])\\cong S_n\\times Aut(C)$ for any $n\\neq 2$, while $Aut(C[2])\\cong S_2\\ltimes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06991","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.06991","created_at":"2026-05-18T00:33:02.507559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06991v2","created_at":"2026-05-18T00:33:02.507559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06991","created_at":"2026-05-18T00:33:02.507559+00:00"},{"alias_kind":"pith_short_12","alias_value":"YB7HQLDQ7JX3","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YB7HQLDQ7JX33PYV","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YB7HQLDQ","created_at":"2026-05-18T12:30:53.716459+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM","json":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM.json","graph_json":"https://pith.science/api/pith-number/YB7HQLDQ7JX33PYVOYOLGDTFXM/graph.json","events_json":"https://pith.science/api/pith-number/YB7HQLDQ7JX33PYVOYOLGDTFXM/events.json","paper":"https://pith.science/paper/YB7HQLDQ"},"agent_actions":{"view_html":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM","download_json":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM.json","view_paper":"https://pith.science/paper/YB7HQLDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06991&json=true","fetch_graph":"https://pith.science/api/pith-number/YB7HQLDQ7JX33PYVOYOLGDTFXM/graph.json","fetch_events":"https://pith.science/api/pith-number/YB7HQLDQ7JX33PYVOYOLGDTFXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM/action/storage_attestation","attest_author":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM/action/author_attestation","sign_citation":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM/action/citation_signature","submit_replication":"https://pith.science/pith/YB7HQLDQ7JX33PYVOYOLGDTFXM/action/replication_record"}},"created_at":"2026-05-18T00:33:02.507559+00:00","updated_at":"2026-05-18T00:33:02.507559+00:00"}