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Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.

Pietro Sabatino (2005)

Revista Matemática Complutense

Let X ⊂ P6 be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15.

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of N is glicci, that is, whether every zero-scheme in 3 is glicci. We show that a general set of n 56 points in 3 admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in 3 .

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