= Order characteristic variety of a Weyl algebra module
{title2=$\operatorname{Ch}_{\mathrm{ord}}(M)=V(\operatorname{Ann}_{\operatorname{gr}R}\operatorname{gr}M)$}
The <algebraic set> defined by the <annihilator of a module> of the <associated graded module> for a <good filtration for the order filtration> is the order characteristic variety. It lies in <affine space> with coordinates $x_1,\ldots,x_n,\xi_1,\ldots,\xi_n$ and is invariant under scaling the $\xi_i$. Its <dimension> is the <dimension of a Weyl algebra module for the order filtration>. The <order filtration of a Weyl algebra> assigns degrees zero to the $x_i$ and one to the $\xi_i$; a characteristic variety formed with the <Bernstein filtration> need not be the same <algebraic set>.
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