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Article

On the Barth-Van de Ven-Tyurin-Sato theorem

Sbornik Mathematics. 2015. Vol. 206. No. 6. P. 814-848.
Penkov I., Tikhomirov A. S.

The Barth-Van de Ven-Tyurin-Sato Theorem states that any finite-rank vector bundle on the complex projective ind-space P∞ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety X which ensure that the same result holds on X. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions. © 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.