Rank 2 vector bundles on ind-Grassmannians

Ivan Penkov; Alexander S. Tikhomirov

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arXiv · 0710.0905

Rank 2 vector bundles on ind-Grassmannians

Ivan Penkov·Alexander S. Tikhomirov

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Abstract

The simplest example of an ind-Grassmannian is the infinite projective space $\mathbf P^\infty$. The Barth-Van de Ven-Tyurin (BVT) Theorem, proved more than 30 years ago \cite{BV}, \cite{T}, \cite{Sa} (see also a recent proof by A. Coandă and G. Trautmann, \cite{CT}), claims that any vector bundle of finite rank on $\mathbf P^\infty$ is isomorphic to a direct sum of line bundles. In the last decade natural examples of infinite flag varieties (or flag ind-varieties) have arisen as homogeneous spaces of locally linear ind-groups, \cite{DPW}, \cite{DiP}. In the present paper we concentrate our attention to the special case of ind-Grassmannians, i.e. to inductive limits of Grassmannians of growing dimension.

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BibTeX RIS

Ivan Penkov, Alexander S. Tikhomirov. 2007-10-03. Rank 2 vector bundles on ind-Grassmannians. https://arxiv.org/abs/0710.0905

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