On incidence between strata of the Hilbert scheme of points on P^2

Details On incidence between strata of the Hilbert scheme of points on P^2 On incidence between strata of the Hilbert scheme of points on P^2

2005-03-31

arxiv.org/abs/math/0503731v1

Mathematics

Algebraic Geometry

23 pages with 8 figures

Scientific paper

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.

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