Definition of very ample divisor
By Sarah Scott •
Sorry for my bad English.
Let $X$ be scheme over $Y$, and $\mathscr{L}$ be invertible sheaf on $X$.
By definition of Hartshorne's algebraic geometry (p120),
$\mathscr{L}$ is very ample relative to $Y$, if there is an immersion $i:X\to \mathbb{P}^r_Y$ for some $r$, such that $i^{*}(\mathscr{O}(1))\cong \mathscr{L}$.
On the other hand, Hartshorne's proof of Iv.Prop.3.1(b) (p307) ,
let $D$ be divisor on curve $X$, $D$ is very ample iff correspond morphism $X\to \mathbb{P}^r_k $ is closed immersion.
Why is tihs? Thanks.
$\endgroup$ 3 Reset to default
