How to show that a form on $\mathbb{C}$ defines a holomorphic $1$-form on $\mathbb{C}/\Gamma$? Can anyone give me a hint on how to start solving this problem?

Let $\Gamma \subset \mathbb{C}$ be a lattice. Show that the form $dz$ on $\mathbb{C}$ defines a holomorphic $1$-form on $\mathbb{C}/\Gamma$.

Any help appreciated!

Thank you for the information provided. Here are some little hints to get you started:


*

*Your idea is the right one. Choose a chart, find the appropriate function, and prove it.

*Your holomorphic $f$ will be in fact $1$.

*Your $Y$ is in fact the whole torus $\mathbb{C}/\Gamma$.


The solution, if you write it down, should look almost trivial. 
