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.
@article{urn:eudml:doc:38173,
title = {Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {363-375},
zbl = {1083.14007},
mrnumber = {MR2166515},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38173}
}
Sabatino, Pietro. Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 363-375. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38173/