Advertisement

manuscripta mathematica

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

Codimension 2 subvarieties of projective space

  • Audun Holme
Article

Abstract

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.

Keywords

Number Theory Projective Space Algebraic Geometry Topological Group Complete Intersection 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations