{"paper":{"title":"Generalized Brotbek's symmetric differential forms and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Song-Yan Xie","submitted_at":"2016-01-19T23:33:43Z","abstract_excerpt":"Over an algebraically closed field $\\mathbb{K}$ with any characteristic, on an $N$-dimensional smooth projective $\\mathbb{K}$-variety $\\mathbf{P}$ equipped with $c\\geqslant N/2$ very ample line bundles $\\mathcal{L}_1,\\dots,\\mathcal{L}_c$, we study the General Debarre Ampleness Conjecture, which expects that for all large degrees $d_1,\\dots,d_c\\geqslant d_0\\gg 1$, for generic $c$ hypersurfaces $\nH_1\\in \\big|\\mathcal{L}_1^{\\,\\otimes\\,d_1}\\big|$, $\\dots$, $H_c\\in \\big|\\mathcal{L}_c^{\\,\\otimes\\,d_c}\\big|$, the complete intersection $X:=H_1 \\cap \\cdots \\cap H_c$ has ample cotangent bundle $\\Omega_X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05133","kind":"arxiv","version":1},"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"}