Boundedness for Threefolds in P6 Containing a Smooth Ruled Surface as Hyperplane Section

Résumé

Let X _ P6 be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant _ 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 _ _. 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.