11. Similarly, a projective variety is the projectivization of the zero set of a collection of homogeneous polynomials . 12. Let I ( Y ) be the homogeneous ideal, generated by the homogeneous polynomials vanishing on Y. 13. One can show that f is a homogeneous polynomial of degree n, therefore it can be written as 14. Like a determinant, the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor. 15. One example is the close relationship between homogeneous polynomials and projective varieties . ( cf . homogeneous coordinate ring .) 16. In 1890, David Hilbert proved a similar statement for the invariants of homogeneous polynomials in any number of variables. 17. A variety is projective if it is defined in some projective space by homogeneous polynomials ( with coefficients in ). 18. When all nonzero coefficients ( including the leading one ) appear as variables, these are homogeneous polynomials of respective degrees 2, 4 and 6. 19. A "'Binomial number "'is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial. 20. One might ask, since the homogeneous polynomials are not really functions on P ( " V " ), what are they, geometrically speaking?
