Suppose I have a complex variety $X$ and two closed subvarieties $A$ and $B$, with closed immersions $i:A\to X$ and $j:B\to X$. Then we have two $\mathcal O_X$-modules $i_*\mathcal O_A$ and $j_*\mathcal O_B$, and we can take their tensor product $i_*\mathcal O_A\otimes j_*\mathcal O_B$. On the other hand we can consider the intersection $A\cap B$, say with inclusion $\iota:A\cap B\to X$, and we have $\iota_*\mathcal O_{A\cap B}$.
I understand that in general we do not have $i_*\mathcal O_A\otimes j_*\mathcal O_B\cong\iota_*\mathcal O_{A\cap B}$, but there are some cases where this holds, e.g. if $A$ and $B$ are disjoint, then both of these sheaves are trivial.
My question is: what are the general conditions under which $i_*\mathcal O_A\otimes j_*\mathcal O_B\cong\iota_*\mathcal O_{A\cap B}$? Is it a kind of transversality?