"projective variety" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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          "langcode": "en",
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          "orig": "en:Algebraic geometry",
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      "examples": [
        {
          "ref": "2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, Springer, page 724",
          "text": "Varieties are sometimes called closed sets and some authors call an open subset of a projective variety a quasiprojective variety. The latter term is in an attempt to unify the concept of affine and projective variety.",
          "type": "quotation"
        },
        {
          "ref": "2006, Werner Ballmann, Lectures on Kähler Manifolds, European Mathematical Society, page 16",
          "text": "A closed subset V#x5C;subset#x5C;mathbb#x7B;C#x7D;Pⁿ is called a (complex) projective variety if, locally, V is defined by a set of complex polynomial equations. Outside of its singular locus, that is, away from the subset where the defining equations do not have maximal rank, the projective variety is a complex submanifold of #x5C;mathbb#x7B;C#x7D;Pⁿ.",
          "type": "quotation"
        },
        {
          "ref": "2015, Katsutoshi Yamanoi, “Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory”, in Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein, editors, Geometry and Analysis on Manifolds: In Memory of Professor Shoshichi Kobayashi, Springer (Birkhäuser), page 209",
          "text": "The central topic of this note is a famous open problem to characterize which projective varieties are Kobayashi hyperbolic.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal."
      ],
      "id": "en-projective_variety-en-noun-f7T7wMFv",
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          "algebraic geometry",
          "algebraic geometry"
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        [
          "Zariski",
          "Zariski"
        ],
        [
          "subvariety",
          "subvariety"
        ],
        [
          "projective space",
          "projective space"
        ],
        [
          "locus",
          "locus"
        ],
        [
          "homogeneous polynomial",
          "homogeneous polynomial"
        ],
        [
          "prime ideal",
          "prime ideal"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
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      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Zariski closed subvariety of a projective space",
          "word": "projektiivinen varisto"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Zariski closed subvariety of a projective space",
          "tags": [
            "feminine"
          ],
          "word": "projektive Varietät"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "Zariski closed subvariety of a projective space",
          "tags": [
            "feminine"
          ],
          "word": "varietà proiettiva"
        }
      ],
      "wikipedia": [
        "projective variety"
      ]
    }
  ],
  "word": "projective variety"
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        {
          "ref": "2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, Springer, page 724",
          "text": "Varieties are sometimes called closed sets and some authors call an open subset of a projective variety a quasiprojective variety. The latter term is in an attempt to unify the concept of affine and projective variety.",
          "type": "quotation"
        },
        {
          "ref": "2006, Werner Ballmann, Lectures on Kähler Manifolds, European Mathematical Society, page 16",
          "text": "A closed subset V#x5C;subset#x5C;mathbb#x7B;C#x7D;Pⁿ is called a (complex) projective variety if, locally, V is defined by a set of complex polynomial equations. Outside of its singular locus, that is, away from the subset where the defining equations do not have maximal rank, the projective variety is a complex submanifold of #x5C;mathbb#x7B;C#x7D;Pⁿ.",
          "type": "quotation"
        },
        {
          "ref": "2015, Katsutoshi Yamanoi, “Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory”, in Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein, editors, Geometry and Analysis on Manifolds: In Memory of Professor Shoshichi Kobayashi, Springer (Birkhäuser), page 209",
          "text": "The central topic of this note is a famous open problem to characterize which projective varieties are Kobayashi hyperbolic.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal."
      ],
      "links": [
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          "algebraic geometry",
          "algebraic geometry"
        ],
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          "subvariety"
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          "projective space",
          "projective space"
        ],
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          "locus",
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        ],
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          "homogeneous polynomial",
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        ],
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          "prime ideal",
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        ]
      ],
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        "(algebraic geometry) A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
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      ]
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  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Zariski closed subvariety of a projective space",
      "word": "projektiivinen varisto"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Zariski closed subvariety of a projective space",
      "tags": [
        "feminine"
      ],
      "word": "projektive Varietät"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "Zariski closed subvariety of a projective space",
      "tags": [
        "feminine"
      ],
      "word": "varietà proiettiva"
    }
  ],
  "word": "projective variety"
}