{"paper":{"title":"Entire holomorphic curves into projective plane intersecting few generic algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Dinh Tuan Huynh, Duc-Viet Vu, Song-Yan Xie","submitted_at":"2017-11-08T15:08:29Z","abstract_excerpt":"For $q\\leq 3$ smooth plane algebraic curves $\\mathcal{C}_i$ having simple normal crossings, if the invariant logarithmic $2$-jet differential bundle associated to $(\\mathbb{P}^2(\\mathbb{C}), \\sum_{i=1}^q \\mathcal{C}_i)$ has a nonzero section vanishing on some ample divisor, then, for every algebraically nondegenerate entire holomorphic curve $f\\colon\\mathbb{C}\\rightarrow\\mathbb{P}^2(\\mathbb{C})$, we have a Second Main Theorem type estimate: \\[ T_f(r) \\leq c\\sum_{i=1}^q\\,N_f^{[1]}(r,\\mathcal{C}_i) + o\\big(T_f(r) \\big)\\parallel, \\] where $T_f(r)$ and $N_f^{[1]}(r,C_i)$ stand for the order functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02996","kind":"arxiv","version":2},"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"}