{"paper":{"title":"Partially complex ranks for real projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico","submitted_at":"2019-06-10T05:56:04Z","abstract_excerpt":"Let $X(\\mathbb {C})\\subset \\mathbb {P}^r(\\mathbb {C})$ be an integral non-degenerate variety defined over $\\mathbb {R}$. For any $q\\in \\mathbb {P}^r(\\mathbb {R})$ we study the existence of $S\\subset X(\\mathbb {C})$ with small cardinality, invariant for the complex conjugation and with $q$ contained in the real linear space spanned by $S$. We discuss the advantages of these additive decompositions with respect to the $X(\\mathbb {R})$-rank, i.e. the rank of $q$ with respect to $X(\\mathbb {R})$. We describe the case of hypersurfaces and Veronese varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03806","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"}