{"paper":{"title":"On the ampleness of the cotangent bundles of complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Song-Yan Xie (LM-Orsay)","submitted_at":"2015-10-21T16:19:22Z","abstract_excerpt":"Based on a geometric interpretation of Brotbek's symmetric differential forms, for the intersection family $\\mathcal{X}$ of generalized Fermat-type hypersurfaces in $\\mathbb{P}_{\\mathbb{K}}^N$ defined over any field $\\mathbb K$, we reconstruct explicit symmetric differential forms by applying Cramer's rule, skipping cohomology arguments, and we further exhibit unveiled families of lower degree symmetric differential forms on all possible intersections of $\\mathcal{X}$ with coordinate hyperplanes.\n  Thereafter, we develop what we call the `moving coefficients method' to prove a conjecture made "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06323","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"}