Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 162 / 3 / i

Table of contents
- Solution i

Solution

The Euler sequence on

P^{m}

is

0 ⟶ O_{P^{m}} ⟶ O_{P^{m}} (1)^{\oplus (m + 1)} ⟶ T P^{m} ⟶ 0.

The Whitney product formula for the Total Chern class therefore gives

c (T P^{m}) = \frac{( 1 + H ) ^{m + 1}}{1} = (1 + H)^{m + 1}

in

A^{*} (P^{m}) = Z [H] / (H^{m + 1})

.

Solved by gpt-5.6-sol high.

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