{"paper":{"title":"Automorphism Groups of Danielewski Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Matthias Leuenberger","submitted_at":"2017-10-17T01:18:31Z","abstract_excerpt":"In this note we study the automorphism group of a smooth Danielewski surface $D_p= \\{(x,y,z) \\in \\mathbb{A}^3 \\mid xy = p(z) \\} \\subset \\mathbb{A}^3$, where $p \\in \\mathbb{C}[z]$ is a polynomial without multiple roots and $deg (p) \\ge 3$. It is known that two such generic surfaces $D_p$ and $D_q$ have isomorphic automorphism groups. Moreover, $\\mathrm{Aut}(D_p)$ is generated by algebraic subgroups and there is a natural isomorphism $\\phi \\colon \\mathrm{Aut}(D_p) \\xrightarrow{\\sim} \\mathrm{Aut}(D_q)$ which restricts to an isomorphism of algebraic groups $G \\xrightarrow{\\sim} \\phi(G)$ for any al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06045","kind":"arxiv","version":1},"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"}