Recent content by hlfmanhoffdor

Ooh, I see now! So the roots of the polynomial F_α are just (X intersect U_0) union (P^n \ U_0) = X union (P^n \U_0). Constructing similar polynomials for U_1, ..., U_n, we have that the zero locus for these polynomials is just the intersection of all the X union (P^n \U_i), which is just X...

I'm having a little trouble seeing something Harris says in his intro book on alg. geom. Say X is contained in P^n. Harris says that X is a projective variety iff X intersect U_i is an affine variety for each i=0,...,n, where U_i are the points [Z_0 , Z_1 , ... , Z_n] in P^n with Z_i =/ 0. I'm a...