On some Gorenstein loci in $\Hilb_{6}(\p 4)$

Details On some Gorenstein loci in $\Hilb_{6}(\p 4)$ On some Gorenstein loci in $\Hilb_{6}(\p 4)$

2006-02-09

arxiv.org/abs/math/0602182v2

Mathematics

Algebraic Geometry

We have improved the exposition and made several minor corrections. To appear in Journal of Algebra

Scientific paper

Let k be an algebraically closed field and let HaG(d) be the open locus inside H(d) (the Hilbert scheme of 0-dimensional length d subschemes of the projective (d-2)-space over k) corresponding to arithmetically Gorenstein subschemes. We prove the irreducibility and characterize the singularities of HaG(6). In order to achieve these results we also classify all Artinian, Gorenstein, not necessarily graded, k-algebras up to degree 6. Moreover we describe the loci in HaG(6) obtained via some geometric construction. Finally we prove the obstructedness of some families of points in HaG(d) for each d>5.

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