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Monads and cohomology modules of rank 2 vector bundles

In: Algebraic Geometry

Author

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  • Wolfram Decker

    (Universität Kaiserslautern, Fachbereich Mathematik)

Abstract

Monads are a useful tool to construct and study rank 2 vector bundles on the complex projective space ℙn, n ≥ 2 (compare [O-S-S]). Horrocks’ technique of eliminating cohomology [Ho 2] represents a given rank 2 vector bundle ℰ as the cohomology of a monad $$ \left( {M\left( \mathcal{E} \right)} \right)\mathcal{A}\xrightarrow{\varphi }\mathcal{B}\xrightarrow{\psi }\varphi $$ as follows.

Suggested Citation

  • Wolfram Decker, 1990. "Monads and cohomology modules of rank 2 vector bundles," Springer Books, in: H. Kurke & J. H. M. Steenbrink (ed.), Algebraic Geometry, pages 7-17, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0685-3_2
    DOI: 10.1007/978-94-009-0685-3_2
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