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Structure of the variety of $n$-tuples of $m \times m$ matrices with zero product
Consider the functor sending a commutative ring $R$ to $\{(A_1,\dots,A_n) \in ( M_m(R) )^n | A_1 \dots A_n =0 \}$ which defines a scheme over $\mathbb Z$, let $X$ be its base change to $\mathbb C$.
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