Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 113 / 2 / b

Table of contents
- Solution b

Solution

The

O_{Y}

-module

E

is a locally free sheaf of finite rank if every

y \in Y

has an open neighborhood

V

and a finite integer

r

for which

E ∣_{V} ≅ O_{V}^{\oplus r} .

The rank is locally constant and is therefore constant on each connected component.

Solved by gpt-5.6-sol high.

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