Stable vector bundle

Summary

A stable vector bundle is a vector bundle whose proper nonzero subbundles all have smaller slope than the bundle itself. The slope of a bundle is its degree divided by its rank. Stability is the condition that makes vector bundles on a curve form a good moduli space. It was introduced by David Mumford in the setting of geometric invariant theory. Over a compact Riemann surface, the Narasimhan–Seshadri theorem identifies stable bundles of degree $0$ with irreducible unitary representations of the fundamental group.