Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur \({\mathbb{P}}_ 2({\mathbb{C}})\)
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 \({\mathbb{P}}_ 2\).
stable vector bundle on projective 2-space
scientific article; zbMATH DE number 3924965