Recovering the good component of the Hilbert scheme
Abstract
In the Hilbert scheme of points on a scheme X there is an open subset parameterizing distinct points. The closure of that open set is by definition the good component. When X is flat over the base, we show that a certain blow-up of the symmetric product of X is the good component. The center of the blow-up we describe by giving generators for its defining ideal. In the non-flat case we obtain similar result by replacing the symmetric product with the divided power product. For smooth surfaces X the good component equals the Hilbert scheme of points.
Keywords
Cite
@article{arxiv.math/0405073,
title = {Recovering the good component of the Hilbert scheme},
author = {Torsten Ekedahl and Roy Skjelnes},
journal= {arXiv preprint arXiv:math/0405073},
year = {2008}
}
Comments
Several sections are rewritten, and results are now in a more general context. In particular flatness, finite type and noetherian assumptions are removed from the main result. Inaccuracies and mistakes have been corrected