See quasi-projective on Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "quasi-", "3": "projective" }, "expansion": "quasi- + projective", "name": "prefix" } ], "etymology_text": "From quasi- + projective, the sense being that projective varieties are closed subsets of projective space while quasi-projective varieties are only required to be locally closed, a strictly weaker condition. The second, scheme-theoretic sense generalizes the first.", "head_templates": [ { "args": { "1": "-" }, "expansion": "quasi-projective (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebraic geometry", "orig": "en:Algebraic geometry", "parents": [ "Algebra", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "69 31", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "72 28", "kind": "other", "name": "English terms prefixed with quasi-", "parents": [], "source": "w+disamb" }, { "_dis": "73 27", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "75 25", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "glosses": [ "Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set." ], "id": "en-quasi-projective-en-adj-6bnlN-Ta", "links": [ [ "algebraic geometry", "algebraic geometry" ], [ "variety", "variety" ], [ "Locally", "locally" ], [ "closed", "closed" ], [ "Zariski topology", "Zariski topology" ], [ "projective n-space", "projective space" ], [ "isomorphic", "isomorphic" ] ], "raw_glosses": [ "(algebraic geometry, of a variety) Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set." ], "raw_tags": [ "of a variety" ], "tags": [ "not-comparable" ], "topics": [ "algebraic-geometry", "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebraic geometry", "orig": "en:Algebraic geometry", "parents": [ "Algebra", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Comprising an open subscheme of a projective scheme" ], "id": "en-quasi-projective-en-adj-TSpIGVs3", "links": [ [ "algebraic geometry", "algebraic geometry" ], [ "scheme", "scheme" ], [ "open", "open" ], [ "subscheme", "subscheme" ], [ "projective", "projective" ] ], "raw_glosses": [ "(algebraic geometry, of a scheme) Comprising an open subscheme of a projective scheme" ], "raw_tags": [ "of a scheme" ], "tags": [ "not-comparable" ], "topics": [ "algebraic-geometry", "geometry", "mathematics", "sciences" ] } ], "wikipedia": [ "Quasi-projective variety" ], "word": "quasi-projective" }
{ "categories": [ "English adjectives", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English terms prefixed with quasi-", "English uncomparable adjectives", "Pages with 1 entry", "Pages with entries" ], "etymology_templates": [ { "args": { "1": "en", "2": "quasi-", "3": "projective" }, "expansion": "quasi- + projective", "name": "prefix" } ], "etymology_text": "From quasi- + projective, the sense being that projective varieties are closed subsets of projective space while quasi-projective varieties are only required to be locally closed, a strictly weaker condition. The second, scheme-theoretic sense generalizes the first.", "head_templates": [ { "args": { "1": "-" }, "expansion": "quasi-projective (not comparable)", "name": "en-adj" } ], "lang": "English", "lang_code": "en", "pos": "adj", "senses": [ { "categories": [ "en:Algebraic geometry" ], "glosses": [ "Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set." ], "links": [ [ "algebraic geometry", "algebraic geometry" ], [ "variety", "variety" ], [ "Locally", "locally" ], [ "closed", "closed" ], [ "Zariski topology", "Zariski topology" ], [ "projective n-space", "projective space" ], [ "isomorphic", "isomorphic" ] ], "raw_glosses": [ "(algebraic geometry, of a variety) Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set." ], "raw_tags": [ "of a variety" ], "tags": [ "not-comparable" ], "topics": [ "algebraic-geometry", "geometry", "mathematics", "sciences" ] }, { "categories": [ "en:Algebraic geometry" ], "glosses": [ "Comprising an open subscheme of a projective scheme" ], "links": [ [ "algebraic geometry", "algebraic geometry" ], [ "scheme", "scheme" ], [ "open", "open" ], [ "subscheme", "subscheme" ], [ "projective", "projective" ] ], "raw_glosses": [ "(algebraic geometry, of a scheme) Comprising an open subscheme of a projective scheme" ], "raw_tags": [ "of a scheme" ], "tags": [ "not-comparable" ], "topics": [ "algebraic-geometry", "geometry", "mathematics", "sciences" ] } ], "wikipedia": [ "Quasi-projective variety" ], "word": "quasi-projective" }
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-28 from the enwiktionary dump dated 2024-11-21 using wiktextract (65a6e81 and 0dbea76). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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