TITLE: When are Hilbert schemes smooth?
QUESTION [13 upvotes]: I know that Hilbert schemes can be very singular. But are there any interesting and nontrivial Hilbert schemes that are smooth? Are there any necessary conditions or sufficient conditions for a Hilbert scheme to be smooth?

REPLY [4 votes]: For some more examples of smooth HS see A.P.Staal: The ubiquity of smooth Hilbert schemes, arxiv AG 31.Jan. 2017.