The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.
@article{bwmeta1.element.bwnjournal-article-bcpv36z1p179bwm,
author = {Str\o mme, Stein},
title = {Elementary introduction to representable functors and Hilbert schemes},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {179-198},
zbl = {0877.14002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p179bwm}
}
Strømme, Stein. Elementary introduction to representable functors and Hilbert schemes. Banach Center Publications, Tome 37 (1996) pp. 179-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p179bwm/
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