M953 Homework 6 Solutions

Due Friday, March 15, 2002

[1] Let R = k[x1, ..., xn] and let Rd denote the subset of all polynomials in R of degree d or less, including 0. Now let S = k[x0, ..., xn] and let Sd denote the subset of all homogeneous polynomials in S of degree d, including 0. Note that both Rd and Sd are k vector spaces. (Part (b) is optional; it's really just for those people who haven't seen "stars and bars" before.)

Solution: [2] In this problem assume, F is in k[x,y], where k is the complex numbers.