Abstract:Long, long ago 1 , in a galaxy 2 far, far away 3 ...The following is the author's PhD Thesis, defended in September 2017. It has not been edited since (except for the footnotes in the open problems section and for this note). In particular, there is nothing here about applications of Białynicki-Birula decomposition to Hilbert schemes [Jel19, Jel20, SS21], the multigraded Hilbert schemes and border apolarity [BB21, Mań20], fiber-full Hilbert schemes [CRR21, CRR22] and other recent developments. Philosophically … Show more
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