{"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 $\\bar{M}_g$. We also show that the map to the Igusa monoidal transform (central cone compactification) is NOT reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3425","kind":"arxiv","version":3},"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"}