Feb 28

The geometry of (tI + (1-t)J) intersect C[x_1...x_n]: it's the projection of (V(I) x 1) union (V(J) x 0), hence V(I) union V(J).

Example: we used this rule to compute the ideal vanishing on the set {(0,0), (1,1)}.

Colon ideals.

V(I : J) = the closure of V(I) \ V(J).
The definition of I : f^{infinity} (which we'll compute next time as an elimination).
Theorem: f is in the radical of I <=> I : f^{infinity} contains 1.