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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)

Abstract

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.

Keywords

Exact Sequence Vector Bundle General Type Complete Intersection Hyperplane Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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