High-degree divisor is very ample on a smooth projective curve
= High-degree divisor is very ample on a smooth projective curve
On a smooth projective curve of genus $g$, every divisor of degree at least $2g+1$ is very ample. Riemann--Roch shows that its sections separate distinct points and tangent directions by comparing $L(D)$ with $L(D-P-Q)$ and $L(D-2P)$.