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Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur \({\mathbb{P}}_ 2({\mathbb{C}})\). (English) Zbl 0578.14013
A construction of the stable and rigid vector bundle on \({\mathbb{P}}_ 2\) is given; they play a crucial role in the determination of the integers r, \(c_ 1, c_ 2\) such that a stable rank r vector bundle of Chern classes \(c_ 1, c_ 2\) exists, and they are called exceptional. This construction is used to build new resolutions of the diagonal of \({\mathbb{P}}_ 2\times {\mathbb{P}}_ 2\). One can then generalize the classical Bejlinson spectral sequence and so give a good description of some coherent sheaves on \({\mathbb{P}}_ 2\).

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
57R20 Characteristic classes and numbers in differential topology
14D20 Algebraic moduli problems, moduli of vector bundles
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