{"paper":{"title":"Algebraically Skew Embeddings of Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andy B. Day","submitted_at":"2025-01-30T04:43:58Z","abstract_excerpt":"Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\\mathbb{P}^N$ such that for any two points $x,y\\in X$, their embedded tangent spaces in $\\mathbb{P}^N$ do not intersect. In this work, we establish an upper bound and a lower bound of the minimal dimension $N$ such that there exists an algebraically skew embedding into $\\mathbb{P}^N$ in terms of the dimension of the given smooth variety $X$. Then we further classify the algebraic curves in terms of their minimal skew embedding dimensions, and apply the same techniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18132","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.18132/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}