Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 152 / 3 / b

Solution

For a torus character

χ^{m}

div (χ^{m}) = \sum_{ρ} ⟨ m, v_{ρ} ⟩ D_{ρ} .

Here

t = x y = χ^{(1, 1)}

, so on the blown-up fan

div (f^{*} t) = D_{e_{1}} + 2 D_{e_{1} + e_{2}} + D_{e_{2}} .

X_{0} = V (f^{*} t)

therefore contains the exceptional divisor

D_{e_{1} + e_{2}}

with multiplicity two. Its defining ideal is not radical along that divisor, so

X_{0}

Solved by gpt-5.6-sol high.

There are no discussions about this article yet.

There are currently no matching articles.