Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of . If X is a projective variety defined by a homogeneous prime ideal I, then the quotient ring
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Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of . If X is a projective variety defined by a homogeneous prime ideal I, then the quotient ring
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En géométrie algébrique, les v ...... ensemble algébrique projectif.
@fr
In algebraic geometry, a proje ...... to areas such as Hodge theory.
@en
In der klassischen algebraisch ...... ynome beschrieben werden kann.
@de
Una varietà proiettiva è l'ins ...... nsieme algebrico (proiettivo).
@it
代数幾何学において，代数閉体 k 上の射影多様体（しゃえいた ...... 手法と代数的な手法の組合せはホッジ理論のような分野に通じる．
@ja
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En géométrie algébrique, les v ...... ensemble algébrique projectif.
@fr
In algebraic geometry, a proje ...... deal I, then the quotient ring
@en
In der klassischen algebraisch ...... ynome beschrieben werden kann.
@de
Una varietà proiettiva è l'ins ...... nsieme algebrico (proiettivo).
@it
代数幾何学において，代数閉体 k 上の射影多様体（しゃえいた ...... 射影的であることは直線束や因子を調べることによって示される．
@ja
label
Projective variety
@en
Projektive Varietät
@de
Varietà proiettiva
@it
Variété algébrique projective
@fr
射影多様体
@ja