Holonomy Groups of Stable Vector Bundles

  • János Kollár

    Fine Hall / Princeton University, USA
  • Vikraman Balaji

    Chennai Mathematical Institute, Siruseri, India


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.

Cite this article

János Kollár, Vikraman Balaji, Holonomy Groups of Stable Vector Bundles. Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, pp. 183–211

DOI 10.2977/PRIMS/1210167326