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Cosa (chi) è projective geometry - definizione
Projective geometry
![The [[Fano plane]] is the projective plane with the fewest points and lines.](https://commons.wikimedia.org/wiki/Special:FilePath/Fano plane.svg?width=200 "The [[Fano plane]] is the projective plane with the fewest points and lines.")
TYPE OF GEOMETRY
Algebraic projective geometry; Projective Geometry; Axioms of projective geometry; History of projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts.
projective geometry
TYPE OF GEOMETRY
Algebraic projective geometry; Projective Geometry; Axioms of projective geometry; History of projective geometry
¦ noun the study of the projective properties of geometric figures.
Projective variety
![An [[elliptic curve]] is a smooth projective curve of genus one.](https://commons.wikimedia.org/wiki/Special:FilePath/Addition on cubic (clean version).svg?width=200 "An [[elliptic curve]] is a smooth projective curve of genus one.")
ALGEBRAIC VARIETY DEFINED WITHIN A PROJECTIVE SPACE
Projective varieties; Projective algebraic variety; Projective curve; Projective surface; Projective scheme; Projective subscheme; Projective algebraic varieties; Projective embedding; Serre vanishing; Projective completion; Projection from a point; Complex projective varieties; Complex projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space \mathbb{P}^n 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 \mathbb{P}^n.
