Let $R$ be a Noetherian ring, $X$ a proper $R$-scheme, $\mathcal{L}$ an ample sheaf and $s \in \Gamma(X, \mathcal{L})$ a global section.
Two questions:
- Why is the open set $X_s := \{x \in X | s_a \neq 0 \}$ affine?
- Is $X_s$ affine under weaker conditions? (for example if $X$ not proper or $\mathcal{L}$ not ample)