{"paper":{"title":"Differential Equations on Complex Projective Hypersurfaces of Low Dimension","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Simone Diverio","submitted_at":"2007-06-07T15:58:57Z","abstract_excerpt":"Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\\mathbb P^{n+1}$. In this paper we find an effective lower bound for the degree of $X$, such that every holomorphic entire curve in $X$ must satisfy an algebraic differential equation of order $k=n=\\dim X$, and also similar bounds for order $k>n$. Moreover, for every integer $n\\ge 2$, we show that there are no such algebraic differential equations of order $k<n$ for a smooth hypersurface in $\\mathbb P^{n+1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1031","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"}