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Let $\{X_i\}$ be a sequence of closed irreducible $k$-dimensional subvarieties of $\mathbb{C}\mathbb{P}^n$ of degree $d$ (they may be assumed to be smooth if necessary). Assume that this sequence ...

Let $\{Z_i\}_{i=1}^\infty$ be a sequence of smooth irreducible $k$-dimensional submanifolds of $\mathbb{C}\mathbb{P}^n$ which converges to a closed subscheme $Z$ in the sense of the Hilbert scheme of $...