= Negative-degree divisor has no sections
{title2=$\deg D<0\Longrightarrow\ell(D)=0$}
If a <divisor on an algebraic curve> $D$ on a <smooth projective curve> has negative <degree of a divisor>, then its <Riemann-Roch space> is zero. Otherwise a nonzero $f\in L(D)$ would make $(f)+D$ an <effective divisor> of degree $\deg D<0$, since a <principal divisor> has degree zero. This is impossible. In <genus> one the <Riemann-Roch theorem> consequently gives $\ell(D)=\deg D$ for every divisor of positive degree.
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