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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.
Sabatino, Pietro. "Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.." Revista Matemática Complutense 18.2 (2005): 363-375. <http://eudml.org/doc/38173>.
@article{Sabatino2005, abstract = {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.}, author = {Sabatino, Pietro}, journal = {Revista Matemática Complutense}, keywords = {Geometría algebraica; 3-Variedades; Subvariedades; Superficies regladas; Intersección; Acotación; low codimensional subvarieties; ruled surface; hyperplane section; degree}, language = {eng}, number = {2}, pages = {363-375}, title = {Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.}, url = {http://eudml.org/doc/38173}, volume = {18}, year = {2005}, }
TY - JOUR AU - Sabatino, Pietro TI - Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section. JO - Revista Matemática Complutense PY - 2005 VL - 18 IS - 2 SP - 363 EP - 375 AB - 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. LA - eng KW - Geometría algebraica; 3-Variedades; Subvariedades; Superficies regladas; Intersección; Acotación; low codimensional subvarieties; ruled surface; hyperplane section; degree UR - http://eudml.org/doc/38173 ER -