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We also show that the map to the Igusa monoidal transform (central cone compactification) is NOT reg"},"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":"1102.3425","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-16T20:48:52Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1be8279b5ee40197897f246f37de0829826932a2d550a2e2112ca26c3acaef82","abstract_canon_sha256":"7cc43b6ab3f4205193564e70520a6a15f24540a7ef8b1af6f12e5ccbf89ca384"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:10.251180Z","signature_b64":"ySrAjGNfGl7lHAT5vmzqoas8+Hp0N80WlySx8D8XmTlBIKkeplF885ncC/cS43b4ZEpyd4vUX8r4wKARsY8yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b17701f77c4d32fbd90efd1afb101614aa7605864573da1cd73c17314d91986","last_reissued_at":"2026-05-18T02:03:10.250500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:10.250500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extending Torelli map to toroidal compactifications of Siegel space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Adrian Brunyate, Valery Alexeev","submitted_at":"2011-02-16T20:48:52Z","abstract_excerpt":"It has been known since the 1970s that the Torelli map $M_g \\to A_g$, associating to a smooth curve its jacobian, extends to a regular map from the Deligne-Mumford compactification $\\bar{M}_g$ to the 2nd Voronoi compactification $\\bar{A}_g^{vor}$.\n  We prove that the extended Torelli map to the perfect cone (1st Voronoi) compactification $\\bar{A}_g^{perf}$ is also regular, and moreover $\\bar{A}_g^{vor}$ and $\\bar{A}_g^{perf}$ share a common Zariski open neighborhood of the image of $\\bar{M}_g$. 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