On some Gorenstein loci in $\Hilb_{6}(\p 4)$
Algebraic Geometry
2007-05-23 v2 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0602182,
title = {On some Gorenstein loci in $\Hilb_{6}(\p 4)$},
author = {Gianfranco Casnati and Roberto Notari},
journal= {arXiv preprint arXiv:math/0602182},
year = {2007}
}
Comments
We have improved the exposition and made several minor corrections. To appear in Journal of Algebra