3-Folds in P5 of Degree 12.
It is proved that there are only finitely many families of codimension two subvarieties not of general type in Q6.
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.
We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of is glicci, that is, whether every zero-scheme in is glicci. We show that a general set of points in 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 .