{"paper":{"title":"Automorphisms of certain affine complements in the projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aleksandr V. Pukhlikov","submitted_at":"2017-03-31T18:10:59Z","abstract_excerpt":"We prove that every biregular automorphism of the affine algebraic variety ${\\mathbb P}^M\\setminus S$, $M\\geqslant 3$, where $S\\subset {\\mathbb P}^M$ is a hypersurface of degree $m\\geqslant M+1$ with a unique singular point of multiplicity $(m-1)$, resolved by one blow up, is a restriction of some automorphism of the projective space ${\\mathbb P}^M$, preserving the hypersurface $S$; in particular, for a general hypersurface $S$ the group $\\mathop{\\rm Aut} ({\\mathbb P}^M\\setminus S)$ is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00018","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"}