 Solution

ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2011/5/b/solution

τ_{λ} [x : y : z] = [z - x : i y : z] .

It fixes

[0 : 1 : 0]

and has an invertible representing matrix. For

X = z - x

Y = i y

Z = z

X (X - Z) (X - (1 - λ) Z) = (z - x) (- x) (λ z - x) = - x (x - z) (x - λ z) = Y^{2} Z .

Hence its restriction is an isomorphism

C_{λ} \to C_{1 - λ}

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