manuscripta mathematica

, Volume 25, Issue 4, pp 323–347

Monads and moduli of vector bundles


  • Wolf Barth
    • Mathematisches InstitutUniversität Erlangen-Nürnberg
  • Klaus Hulek
    • Mathematisches InstitutUniversität Erlangen-Nürnberg

DOI: 10.1007/BF01168047

Cite this article as:
Barth, W. & Hulek, K. Manuscripta Math (1978) 25: 323. doi:10.1007/BF01168047


Horrocks has shown that every vector bundle on ℙ2 and ℙ3 admits a certain “double-ended resolution” by line bundles, which he called a monad. We reprove Horrocks' results taking much care of uniqueness of the monads so obtained. This technique should be useful for constructing moduli spaces of stable vector bundles.

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© Springer-Verlag 1978