{"paper":{"title":"Some Remarks on the Jacobian Conjecture and Dru{\\.z}kowski mappings","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Yan, Michiel de Bondt","submitted_at":"2013-02-24T03:07:57Z","abstract_excerpt":"In this paper, we first show that the Jacobian Conjecture is true for non-homogeneous power linear mappings under some conditions. Secondly, we prove an equivalent statement about the Jacobian Conjecture in dimension $r\\geq 1$ and give some partial results for $r=2$.\n  Finally, for a homogeneous power linear Keller map $F=X+H$ of degree $d \\ge 2$, we give the inverse polynomial map under the condition that $JH^3=0$. We shall show that ${\\operatorname{deg}}(F^{-1})\\leq d^k$ if $k \\le 2$ and $JH^{k+1}=0$, but also give an example with $d = 2$ and $JH^4=0$ such that ${\\operatorname{deg}}(F^{-1})>"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5864","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"}