Cubic Surfaces Jaap Top - Wiskunde

1866, Alfred Clebsch
Theorem. any smooth cubic surface over C is the closure of
ϕ(P 2 (C) − {p 1 , . . . , p 6 }) for certain p 1 , . . . , p 6 ∈ P 2 ,
with ϕ(p) = (f 1 (p) : f 2 (p) : f 3 (p) : f 4 (p)) bijective, and
∑
Cfj = {f ∈ C[x, y, z] homog. of degree 3 & f(p n ) = 0, n = 1, . . . , 6} .
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