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.
|Date of creation||2013-03-22 12:03:58|
|Last modified on||2013-03-22 12:03:58|
|Last modified by||mathcam (2727)|