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It has a partition into manifolds of real dimension $\\le b(m+1)-1$ in which the real rank is constant. A typical rank of $\\sigma_b(X_{m,d}(\\mathbb {C}))(\\mathbb {R})$ is a rank associated to an open part of dimension $b(m+1)-1$. Here we classify all typical ranks when $b\\le 7$ and $d, m$ are not too small. 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