= Clifford inequality for curves
{c}
{title2=$h^0(C,\mathcal L)\leq1+\tfrac12\deg\mathcal L$}
= Clifford's theorem on special divisors
{c}
{synonym}
If a <line bundle> on a <smooth projective curve> has both $h^0(\mathcal L)>0$ and $h^0(\omega_C\otimes\mathcal L^{-1})>0$, the displayed inequality holds. Write these dimensions as $r,s$. The <product dimension bound for sections on a curve> gives $r+s-1\leq g$, and the <Riemann-Roch theorem> gives $r-s=\deg\mathcal L+1-g$. Adding gives $2r\leq\deg\mathcal L+2$.
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