, Volume 25, Issue 4, pp 323-347

Monads and moduli of vector bundles

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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.