Holomorphic normal bundle ( $N_{Y / X}$ )

For a complex submanifold

Y \subseteq X

, the holomorphic normal bundle is the quotient holomorphic vector bundle

N_{Y / X} = TX ∣_{Y} / T Y .

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- Holomorphic conormal sequence Holomorphic normal bundle

Holomorphic conormal sequence

The dual of the tangent-normal sequence is the short exact sequence of holomorphic vector bundles

0 ⟶ N_{Y / X}^{*} ⟶ Ω_{X}^{1} ∣_{Y} ⟶ Ω_{Y}^{1} ⟶ 0.

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Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 118 / 2 / Solution

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