very ample

An invertible sheaf $𝔏$ on a scheme $X$ over a field $k$ is called very ample if (1) at each point $x\in X$, there is a global section $s\in 𝔏(X)$ not vanishing at $x$, and (2) for each pair of points $x,y\in X$, there is a global section $s\in 𝔏(X)$ such that $s$ vanishes at exactly one of $x$ and $y$.

Equivalently, $𝔏$ is very ample if there is an embedding $f:X\to {\mathbb{P}}^n$ such that $f^{*}𝒪(1)=𝔏$, that is, $𝔏$ is the pullback of the tautological bundle on ${\mathbb{P}}^n$.

If $k$ is algebraically closed, Riemann-Roch (http://planetmath.org/RiemannRochTheorem) shows that on a curve $X$, any invertible sheaf of degree greater than or equal to twice the genus of $X$ is very ample.