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This paper investigates the structure of the Hilbert scheme [Formula: see text], which parameterizes [Formula: see text]-point subschemes of a scheme [Formula: see text] formally equivalent to the union of the coordinate axes in [Formula: see text]. Using deformation theory, we provide explicit local defining equations for [Formula: see text] at each point, giving a constructive description of its scheme structure.
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Kim et al. (2026) studied this question.
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