Let $X$ be a variety. A closed subvariety of $X$ is an integral closed subscheme $Z \subset X$. A $k$-cycle on $X$ is a finite formal sum $\sum n_ i [Z_ i]$ where each $Z_ i$ is a closed subvariety of dimension $k$. Whenever we use the notation $\alpha = \sum n_ i[Z_ i]$ for a $k$-cycle we always assume the subvarieties $Z_ i$ are pairwise distinct and $n_ i \not= 0$ for all $i$. In this case the support of $\alpha $ is the closed subset
of dimension $k$. The group of $k$-cycles is denoted $Z_ k(X)$. See Chow Homology, Section 42.8.
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like
$\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.