{"paper":{"title":"On the biregular geometry of the Fulton-MacPherson compactification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alex Massarenti","submitted_at":"2016-03-22T21:27:03Z","abstract_excerpt":"Let $X[n]$ be the Fulton-MacPherson compactification of the configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\\neq 2$ or $\\dim(X)\\geq 2$, then the connected component of the identity of $Aut(X[n])$ is isomorphic to the connected component of the identity of $Aut(X)$. When $X = C$ is a curve of genus $g(C)\\neq 1$ we classify the dominant morphisms $C[n]\\rightarrow C[r]$, and thanks to this we manage to compute the whole automorphism group of $C[n]$, namely $Aut(C[n])\\cong S_n\\times Aut(C)$ for any $n\\neq 2$, while $Aut(C[2])\\cong S_2\\ltimes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06991","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"}