{"paper":{"title":"Forgetful linear systems on the projective space and rational normal curves over $\\cM_{0,2n}^{GIT}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michele Bolognesi","submitted_at":"2009-09-01T11:31:43Z","abstract_excerpt":"Let $\\cM_{0,n}$ the moduli space of $n$-pointed rational curves. The aim of this note is to give a new, geometric construction of $\\cM_{0,2n}^{GIT}$, the GIT compacification of $\\cM_{0,2n}$, in terms of linear systems on $\\PP^{2n-2}$ that contract all the rational normal curves passing by the points of a projective base. These linear systems are a projective analogue of the forgetful maps between $\\bar{\\cM}_{0,2n+1}$ and $\\bar{\\cM}_{0,2n}$. The construction is performed via a study of the so-called $\\textit{contraction}$ maps from the Knudsen-Mumford compactification $\\bar{\\cM}_{0,2n}$ to $\\cM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0151","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"}