Recovering the good component of the Hilbert scheme
成果类型：
Article
署名作者：
Ekedahl, Torsten; Skjelnes, Roy
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2014.179.3.1
发表日期：
2014
页码：
805-841
关键词：
摘要：
We give an explicit construction, for a flat map X -> S of algebraic spaces, of an ideal in the n'th symmetric product of X over S. Blowing up this ideal is then shown to be isomorphic to the schematic closure in the Hilbert scheme of length n subschemesof the locusof n distinct points.This generalizes Haiman's corresponding result for the affine complex plane.However, our construction of the ideal is very different from that of Haiman, using the formalism of divided powers rather than representation theory.In the nonflat case we obtain a similar result by replacing the n'th symmetric product by the n'th divided power product.