%0 Journal Article
%T The locus of points of the Hilbert scheme with bounded regularity
%A Edoardo Ballico
%A Cristina Bertone
%A Margherita Roggero
%J Mathematics
%D 2011
%I arXiv
%R 10.1080/00927872.2014.907905
%X 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 Pl\"ucker embedding.
%U http://arxiv.org/abs/1111.2007v3