{"paper":{"title":"Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Angelo Calil Bianchi, Marcelo Oliveira Veloso","submitted_at":"2015-05-30T20:57:56Z","abstract_excerpt":"We describe the set of all locally nilpotent derivations of the quotient ring $\\mathbb{K}[X,Y,Z]/(f(X)Y - \\varphi(X,Z))$ constructed from the defining equation $f(X)Y = \\varphi(X,Z)$ of a generalized Danielewski surface in $\\mathbb K^3$ for a specific choice of polynomials $f$ and $\\varphi$, with $\\mathbb K$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the $ML$-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of $\\mathbb K$-automorphisms of $\\mathbb K[X,Y,Z]/(f(X)Y - \\varphi(Z))$ als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00164","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"}