An elementary, explicit, proof of the existence of Hilbert schemes of points

2005/06/09 by Trond Gustavsen, Dan Laksov, Gustavsen, Trond +3 · 1 citation
Mathematics · #14C05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:14C05

paper · pdf · doi:10.48550/arxiv.math/0506161

arxiv created 2005/06/09 · arxiv updated 2009/12/01

Abstract

We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of finite type, over any base scheme.

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• The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points

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