# What does this notation mean $\mathcal{H}=\Gamma(\mathbb{C} , \mathcal{L})$ (holomorphic function space)?

What does the $\Gamma$ notation mean in $\mathcal{H}=\Gamma(\mathbb{C} , \mathcal{L})$?

$\mathcal{H}$ is the space of holomorphic functions on $\mathbb{C}$ and $\mathcal{L}$ is the trivial complex line bundle.

What is $\Gamma$? The context is some introduction to geometric quantization of fields using the holomorphic method.

• $\uparrow$ Seen where? – Qmechanic May 18 '18 at 18:03
• $\Gamma$ usually denotes the set of sections. – Qmechanic May 18 '18 at 18:06
• Probably global sections, i.e. sections over the whole complex plane, i.e. entire functions (functions that are everywhere holomorphic) – doetoe May 18 '18 at 18:08