projective variety
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English[edit]
Noun[edit]
projective variety (plural projective varieties)
 (algebraic geometry) A Zariski closed subvariety of a projective space; the zerolocus of a set of homogeneous polynomials that generates a prime ideal.
 2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, Springer, page 724,
 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.
 2006, Werner Ballmann, Lectures on Kähler Manifolds, European Mathematical Society, page 16,
 A closed subset is called a (complex) projective variety if, locally, 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 .
 2015, Katsutoshi Yamanoi, Kobayashi Hyperbolicity and Higherdimensional Nevanlinna Theory, Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein (editors), ', Springer (Birkhäuser), Geometry and Analysis on Manifolds: In Memory of Professor Shoshichi Kobayashi, page 209,
 The central topic of this note is a famous open problem to characterize which projective varieties are Kobayashi hyperbolic.
 2005, Max K. Agoston, Computer Graphics and Geometric Modelling: Mathematics, Springer, page 724,
Translations[edit]
Zariski closed subvariety of a projective space
