Devoir 3 racines

X3−Y2Z= 0
p∈C⊂P2(C) min{k|F(k)̸=
0}F(k)k
p
F(k)=∑
i+j+ℓ=k
∂kF
∂iX∂jY ∂ℓZ(p)XiYjZℓ.
p
p= [0,0,1] F(p)=0
X Y p
Z F
F(p) = FX(p) = FY(p) = 0
FZ(p) = 0
(n−1)FX=XFXX +Y FY X +ZFZX .
p FX=FXX =FY X = 0 FZX (p) = 0
X3+Y3=
XY Z
[1,−ω, 0] ω
[0,0,1]

C
C
C(4 −2)(4 −1)/2 = 3
C
F n G
n+ 1 F G
F+G F +G=AB
A=Ap+Ap+1 +. . . Ap′Aii
B=Bq+Bq+1 +. . . Bq′p=p′q=q′
F G
P2(C)
1 2
P2(C)
5 = 2(2 + 3)/2n= 2 5 = n(n+ 3)/2
n(n+ 3)/2P2(C)
n

nC
(n+2
n)
F, λF PN(C)
N=(n+2
n)−1 = n(n+3) 2n(n+ 3)/2
n