Bezout's Theorem - wiki

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Say, P := (P1, · · · , Pn): C n → C n , assume #P −1 (0) < ∞
Then (introductory lectures, October 2009) ⇒
∞ > dimC
C[x]
=
(P) · C[x]
a∈P−1 dimC
(0)
C[x]a
(P) · C[x]a
deg Pj
Let LPj(x) := HPj(0, x), where HPj(x0, x) := x0 · Pj( x
x0 ).
Assume also {LP1(x) = · · · = LPn(x) = 0} = {0} (∗)
(so called “no solutions at ∞”) for C n ↩→ P n ⇒