THE LOCUS OF POINTS OF THE HILBERT SCHEME WITH BOUNDED REGULARITY

摘要

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 >= 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 <= deg (p(t)) + 2 and linear inequalities in the coordinates of the Plucker embedding