Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.

Pietro Sabatino

Revista Matemática Complutense (2005)

  • Volume: 18, Issue: 2, page 363-375
  • ISSN: 1139-1138

Abstract

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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.

How to cite

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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 -

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