Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

TL;DR

This paper proves that finite rank vector bundles on certain infinite-dimensional algebraic varieties are decomposable into sums of line bundles, extending classical theorems to ind-Grassmannians.

Contribution

It establishes an analogue of the Barth-Van de Ven-Tyurin-Sato theorem for vector bundles on complete intersections in ind-Grassmannians, showing their decomposability.

Findings

Finite rank vector bundles are direct sums of line bundles.

Extension of classical theorems to ind-Grassmannian settings.

Provides structural understanding of vector bundles in infinite-dimensional geometry.

Abstract

In this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem. We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.