{"paper":{"title":"Extended Torelli map to the Igusa blowup in genus 6, 7, and 8","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Catherine Ulrich, Jaeho Shin, Joseph Tenini, Lauren Huckaba, Maxim Arap, Patrick Mcfaddin, Ryan Livingston, Stacy Musgrave, Valery Alexeev, Xiaoyan Hu","submitted_at":"2011-05-23T01:39:01Z","abstract_excerpt":"It was conjectured in \\cite{Namikawa_ExtendedTorelli} that the Torelli map $M_g\\to A_g$ associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli space of stable curves $\\bar{M}_g$ to the (normalization of the) Igusa blowup $\\bar{A}_g^{\\rm cent}$. A counterexample in genus $g=9$ was found in \\cite{AlexeevBrunyate}.\n  Here, we prove that the extended map is regular for all $g\\le8$, thus completely solving the problem in every genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4384","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"}