Let $X$ be a smooth projective surface. Let $p$ be a closed point of $X$. Let $k(p)$ be the corresponding skyscraper sheaf, then actually we could use Grothendieck-Riemann-Roch to calculate the Chern of the coherent sheaf $k(p)$.

However, now let $U\cong \mathrm{Spec}A$ be a open subset containing $p$, $m$ be the maximal idea of $A$ corresponding $p$. Then we have a closed embedding $$i: Y:=\mathrm{Spec}(A/m^2)\to X$$

Now, how do we calculate the Chern class of $i_{*}(\mathcal{O}_{Y})$.

Since $Y$ is not reduced, it seems we could not use GRR. Could you give me some ideas about it? Thanks a lot.