{"paper":{"title":"Homogeneous quasi-translations in dimension 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michiel de Bondt","submitted_at":"2015-01-20T15:31:17Z","abstract_excerpt":"We give a proof in modern language of the following result by Paul Gordan and Max N\\\"other: a homogeneous quasi-translation in dimension $5$ without linear invariants would be linearly conjugate to another such quasi-translation $x + H$, for which $H_5$ is algebraically independent over $\\mathbb C$ of $H_1, H_2, H_3, H_4$. Just like Gordan and N\\\"other, we apply this result to classify all homogeneous polynomials $h$ in $5$ indeterminates from which the Hessian determinant is zero.\n  Others claim to have reproved 'the result of Gordan and N\\\"other in $\\mathbb P^4$' as well, but some of them as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04845","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"}