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arXiv · 1111.2007

The locus of points of the Hilbert scheme with bounded regularity

Edoardo Ballico·Cristina Bertone·Margherita Roggero
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Abstract

In this paper we consider the Hilbert scheme $Hilb_{p(t)}^n$ parameterizing subschemes of $P^n$ with Hilbert polynomial $p(t)$, and we investigate its locus containing points corresponding to schemes with regularity lower than or equal to a fixed integer $r'$. This locus is an open subscheme of $Hilb_{p(t)}^n$ and, for every $s\geq r'$, we describe it as a locally closed subscheme of the Grasmannian $Gr_{p(s)}^{N(s)}$ given by a set of equations of degree $\leq \mathrm{deg}(p(t))+2$ and linear inequalities in the coordinates of the Plücker embedding.

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Edoardo Ballico, Cristina Bertone, Margherita Roggero. 2014-03-18. The locus of points of the Hilbert scheme with bounded regularity. https://doi.org/10.1080/00927872.2014.907905

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