On incidence between strata of the Hilbert scheme of points on $$\mathbb{P}^{2}$$ |
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Authors: | Koen De Naeghel Michel Van den Bergh |
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Institution: | (1) Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium |
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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, Ph.D Thesis, Universite’de Nice,
2002 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.
Michel Van den Bergh is a director of research at the FWO. |
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Keywords: | Projective plane Hilbert scheme of points Incidence Stratification Deformation |
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