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Mar 10, 2017 at 15:56 comment added abx Yes. There is a universal subscheme $Z\subset X\times \mathrm{Hilb}(X)$, hence a proper map $Z\rightarrow \mathrm{Hilb}(X)$, and you are looking at the open subset of the base where the fiber is smooth.
Mar 10, 2017 at 11:04 history asked asv CC BY-SA 3.0