{"paper":{"title":"Birational contraction of genus two tails in the moduli space of genus four curves I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Donghoon Hyeon, Yongnam Lee","submitted_at":"2010-03-21T07:17:05Z","abstract_excerpt":"We show that for $\\alpha \\in (2/3, 7/10)$, the log canonical model $\\bar M_4(\\alpha)$ of the pair $(\\bar M_4, \\alpha \\delta)$ is isomorphic to the moduli space $\\bar M_4^{hs}$ of h-semistable curves, and that there is a birational morphism $\\Xi: \\bar M_4^{hs} \\to \\bar M_4(2/3)$ that contracts the locus of curves $C_1\\cup_p C_2$ consisting of genus two curves meeting in a node $p$ such that $p$ is a Weierstrass point of $C_1$ or $C_2$. To obtain this morphism, we construct a compact moduli space $\\bar M_{2,1}^{hs}$ of pointed genus two curves that have nodes, ordinary cusps and tacnodes as sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3973","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"}