Very ample divisor

A divisor is very ample when its complete linear system defines a closed embedding into projective space.

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 $L(D-2P)$.