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

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.

Keywords

• Vector bundles
• Barth-Van de Ven-Tyurin-Sato theorem
• ind-varieties
• Primary 14M10
• Secondary 14J60
• 32L05