Complex Geometry/Complex and holomorphic vector bundles

Exercises

1. Let $M:=ℂP^n$ and define the tautological line bundle over $ℂP^n$ to be the vector bundle $\tau :=\{([z],x)\in ℂP^n\times ℂ|x\in [z]\}$ with the projection $\pi :([z],x)\mapsto [z]$. Find natural local trivialisations of $\tau$ that turn $\tau$ into a holomorphic line bundle.