{"paper":{"title":"A remark on the codimension of the Green-Griffiths locus of generic projective hypersurfaces of high degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Simone Diverio, Stefano Trapani","submitted_at":"2009-02-21T14:47:42Z","abstract_excerpt":"We show that for every smooth generic projective hypersurface $X\\subset\\mathbb P^{n+1}$, there exists a proper subvariety $Y\\subsetneq X$ such that $\\operatorname{codim}_X Y\\ge 2$ and for every non constant holomorphic entire map $f\\colon\\mathbb C\\to X$ one has $f(\\mathbb C)\\subset Y$, provided $\\deg X\\ge 2^{n^5}$. In particular, we obtain an effective confirmation of the Kobayashi conjecture for threefolds in $\\mathbb P^4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3741","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"}