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The support of the tensor product is the intersection of supports, i.e. $D \cap W$. The support of $Tor^1$ is the union of allthose irreducible components of those $W$ (including embedded components) which are contained in $D$.

The support of the tensor product is the intersection of supports, i.e. $D \cap W$. The support of $Tor^1$ is the union of all irreducible components of those $W$ (including embedded components) which are contained in $D$.

The support of the tensor product is the intersection of supports, i.e. $D \cap W$. The support of $Tor^1$ is the union of those irreducible components of $W$ (including embedded components) which are contained in $D$.

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Sasha
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The support of the tensor product is the intersection of supports, i.e. $D \cap W$. The support of $Tor^1$ is the union of all irreducible components of those $W$ (including embedded components) which are contained in $D$.