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Monads and cohomology modules of rank 2 vector bundles

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Monads and cohomology modules of rank 2 vector bundles COMPOSITIO MATHEMATICA WOLFRAMDECKER Monads and cohomologymodules of rank 2 vector bundles Compositio Mathematica, tome 76, no 1-2 (1990), p. 7-17. <> © Foundation Compositio Mathematica, 1990, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: // implique l’accord avec les conditions gé- nérales d’utilisation ( Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 7- Monads and cohomology modules of rank 2 vector bundles WOLFRAM DECKER* Universitiit Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger-Straße, 6750 Kaiserslautern, FRG Received 19 August 1988; accepted 20 July 1989 Compositio Mathematica 76: 7-17, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands. Introduction 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 6 as the cohomology of a monad as follows. First eliminate the graded S = C[zo,..., zn]-module H103B5(*) = ~m~ZH1(Pn, 03B5(m)) by the universal extension where is given by a minimal system of generators (- stands for sheafification). If n = 2 take this extension as a monad with d = 0. If n 3 eliminate dually Hn-103B5(*) by the universal extension (where Cl = c1(03B5) is the first Chern-class). Then notice, that the two extensions * Partially supported by the DAAD. 8 can be completed to the display of a monad for é. To get a better understanding for é3, 9 and 03C8 consider first th

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