 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-152/2/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

σ = Cone (e_{1}, e_{2}, e_{3})

and all its faces form the standard fan of affine three-space, so

U_{σ} ≅ A^{3} .

The complete target fan has primitive rays

f_{1}, qq u a d f_{2}, qq u a d - f_{1} - f_{2}

and every cone generated by a proper subset of them. This is the two-dimensional simplex fan, hence

X_{Σ} ≅ P^{2} .

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