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, Volume 65, Issue 4, pp 427–446 | Cite as

Codimension 2 subvarieties of projective space

  • Audun Holme


The motivation for the present paper is theHartshorne Conjecture on complete intersections inP n , forn≥6, and in the codimension 2 case: Any smooth codimension 2 subvarietyX ofP n is conjectured to be a complete intersection forn≥6. We prove this conjecture for all varieties with degree below a certain bound, which represents an improvement of the numerical information available untill now.


Number Theory Projective Space Algebraic Geometry Topological Group Complete Intersection 
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  1. [1]
    H. Grauert and M. Schneider. Komplexe Unterräume und holomorfe Vektorraumbündel vom Rang zwei.Mathematische Annalen, 1977Google Scholar
  2. [2]
    R. Hartshorne. Stable vector bundles of rank 2 onP 3.Mathematische Annalen, 238:229–280, 1978Google Scholar
  3. [3]
    A. Holme.Chern numbers of codimension 2 subvarieties of P N,N≥6. Preprint Series Department of Mathematics University of Bergen, 1983Google Scholar
  4. [4]
    A. Holme.On nillpotent subcanonical schemes in P n, Preprint. To appear, 1989Google Scholar
  5. [5]
    A. Holme.On Linear Subspaces with Nilpotent Structure. 1989. Preprint. To appear, 1989Google Scholar
  6. [6]
    A. Holme and M. Schneider. A computer aided approach to codimension 2 subvarieties ofP n n≥6.Journal für die reine und angewandte Mathematik, 357:205–220, 1985Google Scholar
  7. [7]
    Z. Ran. On projective varieties of codimension 2.Inventiones Mathematicae, 73:333–336, 1983Google Scholar
  8. [8]
    T. Sauer. Nonstable reflexive sheaves onP 3.Transactions of the American Mathematical Society, 281:633–655, 1984Google Scholar
  9. [9]
    J.- P. Serre.Algebre Locale. Multiplicités. Volume 340 ofLecture Notes in Mathematics, Springer Verlag, Berlin, Heidelberg, New York, 1973Google Scholar
  10. [10]
    R. Speiser. Vanishing criteria and the picard group for projective varieties of low codimension.Compositio Mathematica, 42:13–21, 1981Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Audun Holme
    • 1
  1. 1.Matematisk Institutt Allégaten 55Universitetet i BergenBergenNorway

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