{"paper":{"title":"Is the affine space determined by its automorphism group?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Hanspeter Kraft, Immanuel van Santen n\\'e Stampfli","submitted_at":"2017-07-21T13:12:58Z","abstract_excerpt":"In this note we study the problem of characterizing the complex affine space $\\mathbb{A}^n$ via its automorphism group. We prove the following. Let $X$ be an irreducible quasi-projective $n$-dimensional variety such that $\\mathrm{Aut}(X)$ and $\\mathrm{Aut}(\\mathbb{A}^n)$ are isomorphic as abstract groups. If $X$ is either quasi-affine and toric or $X$ is smooth with Euler characteristic $\\chi(X) \\neq 0$ and finite Picard group $\\mathrm{Pic}(X)$, then $X$ is isomorphic to $\\mathbb{A}^n$.\n  The main ingredient is the following result. Let $X$ be a smooth irreducible quasi-projective variety of d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06883","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"}