{"paper":{"title":"Automorphisms of $\\mathbb{C}^3$ Commuting with a $\\mathbb{C}^+$-Action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Immanuel Stampfli","submitted_at":"2014-06-24T14:15:43Z","abstract_excerpt":"Let $\\rho$ be an algebraic action of the additive group $\\mathbb{C}^+$ on the three-dimensional affine space $\\mathbb{C}^3$. We describe the group $\\textrm{Cent}(\\rho)$ of polynomial automorphisms of $\\mathbb{C}^3$ that commute with $\\rho$. A particular emphasis lies in the description of the automorphisms in $\\textrm{Cent}(\\rho)$ coming from algebraic $\\mathbb{C}^+$-actions. As an application we prove that the automorphisms in $\\textrm{Cent}(\\rho)$ that are the identity on the algebraic quotient of $\\rho$ form a characteristic subgroup of $\\textrm{Cent}(\\rho)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6246","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"}