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We study linearly dependent subsets with prescribed cardinality $s$ of a multiprojective space. If the set $S$ is a circuit, there is an upper bound on the number of factors of the minimal multiprojective space containing $S$. B. Lovitz gave a sharp upper bound for this number. If $S$ has higher dependency, this may be not true without strong assumptions (and we give examples and suitable assumptions). We describe the dependent subsets $S$ with $\#S=6$.
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