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

Pietro SABATINO
Università degli Studi di Roma “Tor Vergata”
Dipartimento di Matematica
Via della Ricerca Scientifica 1
00133 Roma — Italy
sabatino@axp.mat.uniroma2.it

Received: September 7, 2004
Accepted: March 9, 2005
ABSTRACT

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

Key words: threefolds, low codimensional subvarieties, ruled surface as hyperplane section, bounded degree.
2000 Mathematics Subject Classification: Primary 14C05, 14M07, 14M10; Secondary 14J19.