On the Gorenstein locus of some punctual Hilbert schemes

Details On the Gorenstein locus of some punctual Hilbert schemes On the Gorenstein locus of some punctual Hilbert schemes

2008-03-07

arxiv.org/abs/0803.1135v2

Mathematics

Algebraic Geometry

The exposition has been improved and some of the main results have been extended to degree $d\le 9$

Scientific paper

Let $k$ be an algebraically closed field and let $\Hilb_{d}^{G}(\p{N})$ be the open locus of the Hilbert scheme $\Hilb_{d}(\p{N})$ corresponding to Gorenstein subschemes. We prove that $\Hilb_{d}^{G}(\p{N})$ is irreducible for $d\le9$, we characterize geometrically its singularities for $d\le 8$ and we give some results about them when $d=9$ which give some evidence to a conjecture on the nature of the singular points in $\Hilb_{d}^{G}(\p{N})$.

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