Long ago when I was in grad school I was told that Grothendieck's construction of the Hilbert scheme is rooted in two main technical points: Castelnuovo-Mumford regularity and Mumford flattening stratification. In grad school I made sure to learn these two constructions very carefully, and I have been dealing with the Hilbert scheme (mostly of points in the plane) closely in my work since then, but I still don't understand at all on a philosophical level why the Hilbert scheme exists and why these two technical constructions play the main role in its existence. Could someone enlighten me regarding these questions? In general, why is the subject of Hilbert schemes so insanely technical if they are so incredibly useful in mathematics, and what could be a 'correct' point of view on Hilbert schemes which would make them easier to understand from the philosophical perspective? What would be good suggestions for literature which could help to understand the technicalities of the subject of Hilbert schemes on a more philosophical level?

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