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

Abstract

The Barth-Van de Ven-Tyurin-Sato Theorem claims that any finite rank vector bundle on the infinite complex projective 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. Keywords: ind-variety, vector bundle

26 pages

References in corpus (2)

• Ind--varieties of generalized flags as homogeneous spaces for classical ind--groups
• Finite rank vector bundles on inductive limits of grassmannians

Cited by in corpus (1)

• Ind-varieties of generalized flags: a survey of results