Stable Vector Bundle
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High Quality Content by WIKIPEDIA articles! In mathematics, a stable vector bundle is a vector bundle that is stable in the sense of geometric invariant theory. They were defined by Mumford (1963).Narasimhan & Seshadri (1965) showed that stable bundles on projective nonsingular curves are the same as those that have projectively flat unitary irreducible connections; these correspond to irreducible unitary representations of the fundamental group. Kobayashi and Hitchin conjectured an analogue of this in higher dimensions; this was proved for projective nonsingular surfaces by Donaldson (1985), ...
High Quality Content by WIKIPEDIA articles! In mathematics, a stable vector bundle is a vector bundle that is stable in the sense of geometric invariant theory. They were defined by Mumford (1963).Narasimhan & Seshadri (1965) showed that stable bundles on projective nonsingular curves are the same as those that have projectively flat unitary irreducible connections; these correspond to irreducible unitary representations of the fundamental group. Kobayashi and Hitchin conjectured an analogue of this in higher dimensions; this was proved for projective nonsingular surfaces by Donaldson (1985), who showed that in this case a vector bundle is stable if and only if it has an irreducible Hermitian-Einstein connection.
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