Exercise 111.66.7. Let $X$ be a smooth projective curve over an algebraically closed field $k$ of genus $g \geq 100$. What values can $h^0(\mathcal{L}) = \dim _ k H^0(X, \mathcal{L})$ take for $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module of degree $2g - 4$ on $X$? Answer as completely as you can.
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