Abstract
We give a condition in terms of the possible graded Betti numbers compatible with a given Hilbert functionH of 0-dimensional subschemes of ℙn which implies the reducibility of the postulation Hilbert scheme and of its subscheme which parametrizes reduced subschemes with Hilbert functionH.
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References
Campanella G.,Standard bases of perfect homogeneous polynomial ideals of height 2, J. Algebra,101 (1986), 47–60.
Charalambous H., Evans E. G.Resolutions with a given Hilbert function, Contemp. Math.,159 (1994), 19–26.
Gotzmann G.,A stratification of the Hilbert scheme of points in the projective plane, Math. Z.,199 (4) (1988), 539–547.
Hartshorne R.,Algebraic geometry, Springer-Verlag, GTM 52 (1977).
Hulett H. A.,Maximum Betti Numbers of Homogeneous Ideals with a Given Hilbert Function, Comm. in Alg.,21 (7) (1993), 2335–2350.
Kleppe J. O.,Maximal families of Gorenstein algebras, Preprint.
Iarrobino A.,Hilbert Scheme of points: overview of last ten years, Proc. Sympos. Pure Math.,46, part 2, Amer. Math. Soc., Providence, RI, (1987).
Iarrobino A., Kanev V.,Power Sums, Gorenstein Algebras, and Determinantal Loci, Springer-Verlag, LNM 1721 (1999).
Mall D.,Connectedness of Hilbert function strata and other connectedness results, J. of Pure and Applied Algebra,150 (2000), 175–205.
Pardue K.,Deformations of graded modules and connected loci on the Hilbert scheme, The Curves Seminar at Queen’s, Vol. XI, Queen’s Papers in Pure and Appl. Math.,105 (1997), 131–139.
Richert B.,Smallest graded betti numbers, J. Algebra,204 (2001), 236–259.
Ragusa A., Zappalà G.,Partial Gorenstein in Codimension 3, Le Matematiche,55 (2000) II, 353–371.