X-Nico

Global section functor

Let $\backslash mathcal\; O\; X$ be the sheaf of holomorphic functions on the compact connected complex manifold X, then by the maximum principle, global sections are constant, ie. $\backslash Gamma\; (X,\; \backslash mathcal\; O\; X)\; =\; \backslash mathbb\; C$

see also