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I am learning about cycles on schemes, and I am wondering how I can think about a $0$-cycle, $1$-cycle (or more generally, $r$-cycle) geometrically?

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    $\begingroup$ This is pretty much the definition, but a $0$-cycle is basically a set of (closed) points, each with a multiplicity. Same thing with an $r$-cycle: it is a set of $r$-dimensional subvarieties, with multiplicity. $\endgroup$ Mar 5, 2020 at 16:13

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