{"paper":{"title":"Effective algebraic degeneracy of entire curves in complements of smooth projective hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Lionel Darondeau","submitted_at":"2014-02-06T16:32:28Z","abstract_excerpt":"In this work, it is established that for a generic projective hypersurface $H\\subset\\mathbb{P}^n(\\mathbb{C})$ of degree $d\\geq(5n)^2\\,n^{n}$, any holomorphic entire curve $f\\colon\\mathbb{C}\\to\\mathbb{P}^n(\\mathbb{C})\\setminus H$ has its image contained in a proper algebraic subvariety $Z\\subsetneq\\mathbb{P}^{n}(\\mathbb{C})$, that does not depend on the curve $f$.\n  Here generic means that the coefficients of the defining equation of $H$ have to lie outside of a proper algebraic subvariety of the projective space of coefficients of homogeneous polynomials of degree $d$ (that parametrizes the al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1396","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"}