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The collection $\\Mf(J)$ of the homogeneous polynomial ideals $I$, such that the monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\\em $J$-marked family}. It can be endowed with a structure of affine scheme, called a {\\em $J$-marked scheme}. For special ideals $J$, $J$-marked schemes provide an open cover of the Hilbert scheme $\\hilbp$, where $p(t)$ is the Hilbert polynomial of $S/J$. 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