In this paper we consider the Hilbert scheme 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 and, for every s ≥ r′, we describe it as a locally closed subscheme of the Grasmannian given by a set of equations of degree ≤deg(p(t)) +2 and linear inequalities in the coordinates of the Plücker embedding.
The Locus of Points of the Hilbert Scheme with Bounded Regularity / Ballico, Edoardo; Bertone, Cristina; Roggero, Margherita. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 43:7(2015), pp. 2912-2931. [10.1080/00927872.2014.907905]
The Locus of Points of the Hilbert Scheme with Bounded Regularity
Ballico, Edoardo;
2015-01-01
Abstract
In this paper we consider the Hilbert scheme 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 and, for every s ≥ r′, we describe it as a locally closed subscheme of the Grasmannian given by a set of equations of degree ≤deg(p(t)) +2 and linear inequalities in the coordinates of the Plücker embedding.| File | Dimensione | Formato | |
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