Boundedness for Nongeneral-Type 3-Folds in ℙ5

  • Robert Braun
  • Giorgio Ottaviani
  • Michael Schneider
  • Frank Olaf Schreyer
Part of the The University Series in Mathematics book series (USMA)


One of the tantalizing problems in projective geometry is Hartshorne’s conjecture: smooth subvarieties X ⊂n(ℂ) with dim \(>\frac{2} {3}n \) are complete intersections. Due to Serre’s correspondence the most interesting case is codim X = 2. In fact, in this case even 4-folds in ℙ6 should be complete intersections. For n ≤ 5 the remaining cases of “low codimension” are surfaces in ℙ4 and 3-folds in ℙ5. For surfaces in ℙ4, Ellingsrud and Peskine [8] have established the following beautiful boundedness result.


Exact Sequence Vector Bundle General Type Complete Intersection Hyperplane Section 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Robert Braun
    • 1
  • Giorgio Ottaviani
    • 2
  • Michael Schneider
    • 1
  • Frank Olaf Schreyer
    • 2
  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany
  2. 2.Dipartimento di MatematicaII Università di RomaRomaItaly

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