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# Chern classes of ideal sheaf of an analytic subetsubset

Hello,

Here's my question : 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:

$$c_k(\mathcal{I}_Z) = (-1)^k(k-1)![Z]$$

The form of the expression suggests using GRR, but I cannot figure out how. Does anyone know a proof for this (or at least an online reference). ?

Thanks.

1

# Chern classes of ideal sheaf of an analytic subet

Hello,

Here's my question : 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:

$$c_k(\mathcal{I}_Z) = (-1)^k(k-1)![Z]$$

The form of the expression suggests using GRR, but I cannot figure out how. Does anyone know a proof for this (or at least an online reference).

Thanks.