Lemma 42.55.4. In the situation of Lemma 42.55.3 say $\dim _\delta (X) = n$. Then we have

$c_ t(Z \to X, i_*\mathcal{O}_ Z) \cap [X]_ n = 0$ for $t = 1, \ldots , r - 1$,

$c_ r(Z \to X, i_*\mathcal{O}_ Z) \cap [X]_ n = (-1)^{r - 1}(r - 1)![Z]_{n - r}$,

$ch_ t(Z \to X, i_*\mathcal{O}_ Z) \cap [X]_ n = 0$ for $t = 0, \ldots , r - 1$, and

$ch_ r(Z \to X, i_*\mathcal{O}_ Z) \cap [X]_ n = [Z]_{n - r}$.

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