Abstract
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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References
Atiyah,M.F.,Ward,R.S.: Instantons and algebraic geometry. Commun.Math.Phys. 55, 117–124 (1977)
Atiyah,M.F., Drinfeld,V.G., Hitchin,N.J., Manin,Yu.I.: Construction of instantons. Preprint, Oxford 1978
Barth,W.: Moduli of vector bundles on the projective plane. Inv.math., 42, 63–91 (1977)
Barth, W., Elencwajg, G.: To appear
Godement,T.: Topologie algébrique et théorie des faisceaux. Hermann, Paris, 1958
Horrocks,G.: Vector bundles on the punctured spectrum of a local ring. Proc.London Math.Soc. 14, 689–713 (1964)
Horrocks,G.: Letter to Mumford, 1971, unpublished
Horrocks,G.: Construction of bundles on Pn. In Séminaire Douady-Verdier. Ec.Norm.Sup. Paris (1977)
Hulek,K.: Forthcoming thesis
Takemoto,F.: Stable bundles on algebraic surfaces. Nagoya Math. J., 47, 29–48 (1972)
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Barth, W., Hulek, K. Monads and moduli of vector bundles. Manuscripta Math 25, 323–347 (1978). https://doi.org/10.1007/BF01168047
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DOI: https://doi.org/10.1007/BF01168047
