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This tag is used if a reference is needed in a paper or textbook on a specific result.

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Reference request: is the punctual Hilbert scheme irreducible?

It is certainly not irreducible if n=8 and d>3. This is analyzed nicely in the paper Hilbert schemes of 8 points, Dustin A. Cartwright, Daniel Erman, Mauricio Velasco, Bianca Viray available at htt …
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Are the arithmetic genera of Cohen-Macaulay curves in a fixed homology class bounded?

EDIT: As Angelo mentions, the argument below has a problem in the case of non-reduced curves. I am not sure that an upper bound for the arithmetic genus is impossible to show, but certainly the lower …
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