On incidence between strata of the Hilbert scheme of points on P^2
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Abstract
The Hilbert scheme of n points in the projective plane has a natural stratification obtained from the associated Hilbert series. In general, the precise inclusion relation between the closures of the strata is still unknown. Guerimand studied this problem for strata whose Hilbert series are as close as possible. Preimposing a certain technical condition he obtained necessary and sufficient conditions for the incidence of such strata. In this paper we present a new approach, based on deformation theory, to Guerimand's result. This allows us to show that the technical condition is not necessary.
Cite
@article{arxiv.math/0503731,
title = {On incidence between strata of the Hilbert scheme of points on P^2},
author = {K. De Naeghel and M. Van den Bergh},
journal= {arXiv preprint arXiv:math/0503731},
year = {2007}
}
Comments
23 pages with 8 figures