Holonomy groups of stable vector bundles

Details Holonomy groups of stable vector bundles Holonomy groups of stable vector bundles

2006-01-06

arxiv.org/abs/math/0601120v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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