View source for Complex Geometry/Complex and holomorphic vector bundles

== Exercises ==
#Let <math>M := \mathbb C P^n</math> and define the ''tautological line bundle'' over <math>\mathbb C P^n</math> to be the vector bundle <math>\tau := \{([z], x) \in \mathbb C P^n \times \mathbb C| x \in [z]\}</math> with the projection <math>\pi: ([z], x) \mapsto [z]</math>. Find natural local trivialisations of <math>\tau</math> that turn <math>\tau</math> into a holomorphic line bundle.

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