JournalsprimsVol. 44 , No. 2DOI 10.2977/prims/1210167326

Holonomy Groups of Stable Vector Bundles

  • János Kollár

    Fine Hall / Princeton University, USA
  • Vikraman Balaji

    Chennai Mathematical Institute, Siruseri, India
Holonomy Groups of Stable Vector Bundles cover

Abstract

We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan–Seshadri unitary representation of its restriction to curves.

Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.