projective variety
Given a homogeneous polynomial of degree in variables and a point , we cannot evaluate at that point, because it has multiple such representations, but since we can say whether any such representation (and hence all) vanish at that point.
A projective variety over an algebraically closed field is a subset of some projective space over which can be described as the common vanishing locus of finitely many homogeneous polynomials with coefficients in , and which is not the union of two such smaller loci. Also, a quasi-projective variety is an open subset of a projective variety.
Title | projective variety |
Canonical name | ProjectiveVariety |
Date of creation | 2013-03-22 12:03:58 |
Last modified on | 2013-03-22 12:03:58 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 9 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 14-00 |
Related topic | AffineVariety |
Related topic | Scheme |
Related topic | AlgebraicGeometry |
Related topic | Variety |
Related topic | ChowsTheorem |
Defines | quasi-projective variety |