{"paper":{"title":"Real identifiability vs complex identifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristiano Bocci, Elena Angelini, Luca Chiantini","submitted_at":"2016-08-25T15:34:39Z","abstract_excerpt":"Let $T$ be a real tensor of (real) rank $r$. $T$ is 'identifiable' when it has a unique decomposition in terms of rank $1$ tensors. There are cases in which the identifiability fails over the complex field, for general tensors of rank $r$. This behavior is quite peculiar when the rank $r$ is submaximal. Often, the failure is due to the existence of an elliptic normal curve through general points of the corresponding Segre, Veronese or Grassmann variety. We prove the existence of nonempty euclidean open subsets of some variety of tensors of rank $r$, whose elements have several decompositions o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07197","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"}