{"paper":{"title":"Rational maps $H$ for which $K(tH)$ has transcendence degree 2 over $K$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Michiel de Bondt","submitted_at":"2015-01-24T14:24:39Z","abstract_excerpt":"We classify all rational maps $H \\in K(x)^n$ for which ${\\rm trdeg}_K K(tH_1,tH_2,\\ldots,tH_n) \\le 2$, where $K$ is any field and $t$ is another indeterminate.\n  Furthermore, we classify all such maps for which additionally $JH \\cdot H = {\\rm tr} JH \\cdot H$ (where $JH$ is the Jacobian matrix of $H$), i.e. $$ \\sum_{i=1}^n H_i \\frac{\\partial}{\\partial x_i} H_k = \\sum_{i=1}^n H_k \\frac{\\partial}{\\partial x_i} H_i $$ for all $k \\le n$. This generalizes a theorem of Paul Gordan and Max N\\\"other, in which both sides and the characteristic of $K$ are assumed to be zero.\n  Besides this, we use some o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06046","kind":"arxiv","version":4},"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"}