{"paper":{"title":"Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree","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":"2017-04-11T15:32:46Z","abstract_excerpt":"In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\\colon\\mathbb{C}\\rightarrow\\mathbb{P}^n(\\mathbb{C})$, in present of a {\\sl generic} hypersuface $D\\subset\\mathbb{P}^n(\\mathbb{C})$ of sufficiently high degree $d\\geq 15(5n+1)n^n$: \\[ T_f(r) \\leq \\,N_f^{[1]}(r,D) + O\\big(\\log T_f(r) + \\log r \\big)\\parallel, \\] where $T_f(r)$ and $N_f^{[1]}(r,D)$ stand for the order function and the $1$-truncated counting function in Nevanlinna theory. This inequality quantifies recent results on the logarithmic Green--Grif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03358","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"}