Wednesday, 14 August 2013

Effective Cartier divisors

Effective Cartier divisors

A Cartier divisor on a scheme $X$ is effective if it can be represented by
$\{(U_i,f_i)\}$ where $U_i$ covers $X$ and $f_i \in X$ Let $\mathcal{I}$
be a sheaf of ideals which is locally generated by $f_i$. I know that
$\mathcal{I}$ defines the closed subscheme, say $Y$
In Hartshorne book, $Y$ has codimension $1$. But I don't know why $Y$ has
codimension $1$.

No comments:

Post a Comment