{"paper":{"title":"Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Jean-Pierre Demailly (IF)","submitted_at":"2015-01-28T08:47:35Z","abstract_excerpt":"The Green-Griffiths-Lang conjecture stipulates that for every projective variety $X$ of general type over ${\\mathbb C}$, there exists a proper algebraic subvariety of $X$ containing all non constant entire curves $f:{\\mathbb C}\\to X$.  Using the formalism of directed varieties, we prove here that this assertion holds true in case $X$ satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle $T\\_X$. We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurfac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07625","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"}