Let $X$ be a Kähler manifold of dimension $n$, and $Z \subset X$ an analytic subset of codimension $k$. I have read in a paper the following result, a proof of which I cannot find:


$$c\_k(\mathscr{I}\_Z) = (-1)^k(k-1)![Z]$$


The form of the expression suggests using GRR, but I cannot figure out how. 



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> Does anyone know a proof for this (or at least an online reference)?
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Chern classes of ideal sheaf of an analytic subset
In Fulton's book *Intersection Theory*, Theorem 15.3 and Example 15.3.1 (p. 297 of my edition) it is proven, by using GRR, that $$c\_k(\mathscr{O}\_Z)=(-1)^{k-1}(k-1)![Z].$$
By using the short exact sequence
$$0 \to \mathscr{I}\_Z \to \mathscr{O}\_X \to \mathscr{O}\_Z \to 0$$
we obtain $1=c(\mathscr{O}\_X)=c(\mathscr{O}\_Z)c(\mathscr{I}\_Z)$ and this in turn implies $$c\_k(\mathscr{I}\_Z)=(-1)^k (k-1)![Z].$$ 


