{"paper":{"title":"Cartan's Conjecture for Moving Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangsheng Yu, Qiming Yan","submitted_at":"2017-06-19T11:58:41Z","abstract_excerpt":"Let $f$ be a holomorphic curve in $\\mathbb{P}^n({\\mathbb{C}})$ and let $\\mathcal{D}=\\{D_1,\\ldots,D_q\\}$ be a family of moving hypersurfaces defined by a set of homogeneous polynomials $\\mathcal{Q}=\\{Q_1,\\ldots,Q_q\\}$. For $j=1,\\ldots,q$, denote by $Q_j=\\sum\\limits_{i_0+\\cdots+i_n=d_j}a_{j,I}(z)x_0^{i_0}\\cdots x_n^{i_n}$, where $I=(i_0,\\ldots,i_n)\\in\\mathbb{Z}_{\\ge 0}^{n+1}$ and $a_{j,I}(z)$ are entire functions on ${\\mathbb{C}}$ without common zeros. Let $\\mathcal{K}_{\\mathcal{Q}}$ be the smallest subfield of meromorphic function field $\\mathcal{M}$ which contains ${\\mathbb{C}}$ and all $\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05896","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"}