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. 183–211DOI 10.2977/PRIMS/1210167326