In this paper we consider the Hilbert scheme Hilbnp(t) parameterizing subschemes of Pn 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 Hilbnp(t) and, for every s≥r′, we describe it as a locally closed subscheme of the Grasmannian GrN(s)p(s) given by a set of equations of degree ≤deg(p(t))+2 and linear inequalities in the coordinates of the Pl\"ucker embedding.
THE LOCUS OF POINTS OF THE HILBERT SCHEME WITH BOUNDED REGULARITY
BERTONE, Cristina;ROGGERO, Margherita
2015-01-01
Abstract
In this paper we consider the Hilbert scheme Hilbnp(t) parameterizing subschemes of Pn 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 Hilbnp(t) and, for every s≥r′, we describe it as a locally closed subscheme of the Grasmannian GrN(s)p(s) given by a set of equations of degree ≤deg(p(t))+2 and linear inequalities in the coordinates of the Pl\"ucker embedding.
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