Standard reference:
$% P. Sabatino, Boundedness for threefolds in P6 containing a smooth ruled surface
as hyperplane section, Rev. Mat. Complut. 18 (2005), no. 2, 363–375.%$
Boundedness for Threefolds in P6 Containing a Smooth Ruled Surface as Hyperplane Section
Let
be a smooth irreducible projective threefold, and
its degree.
In this paper we prove that there exists a constant
such that for all
containing a smooth ruled surface as hyperplane section and not contained in a
fourfold of degree less than or equal to
,
. 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
.
Key words: threefolds, low codimensional subvarieties, ruled surface as hyperplane
section, bounded degree.
2000 Mathematics Subject Classification: Primary 14C05, 14M07, 14M10; Secondary
14J19.