Geodesic
On the Barth-Van de Ven-Tyurin-Sato theorem
Sbornik. Mathematics, Tome 206 (2015) no. 6, pp. 814-848

Voir la notice de l'article provenant de la source Math-Net.Ru

The Barth-Van de Ven-Tyurin-Sato Theorem states that any finite-rank vector bundle on the complex projective ind-space $\mathbf{P}^\infty$ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety $\mathbf{X}$ which ensure that the same result holds on $\mathbf{X}$. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions. Bibliography: 18 titles.
Keywords: ind-variety, vector bundle. 
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I. B. Penkov; A. S. Tikhomirov. On the Barth-Van de Ven-Tyurin-Sato theorem. Sbornik. Mathematics, Tome 206 (2015) no. 6, pp. 814-848. http://geodesic.mathdoc.fr/item/SM_2015_206_6_a2/