Complex Geometry/Complex and holomorphic vector bundles
Exercises edit
- Let and define the tautological line bundle over to be the vector bundle with the projection . Find natural local trivialisations of that turn into a holomorphic line bundle.
and define the tautological line bundle over 
to be the vector bundle ![{\displaystyle \tau :=\{([z],x)\in \mathbb {C} P^{n}\times \mathbb {C} |x\in [z]\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b53f51e9c637add03a6db6989af3b578b256f33b)
with the projection ![{\displaystyle \pi :([z],x)\mapsto [z]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3be862662a174495b8d2f37fdcaf893ffa00e29c)
. Find natural local trivialisations of 
that turn into a holomorphic line bundle.