Einstein Type Metrics and Stability on Vector Bundles
نویسنده
چکیده
In this paper we show that stability for holomorphic vector bundles are equivalent to the existence of solutions to certain system of Monge Amp ere equations parametrized by a parameter k. We solve this fully nonlinear elliptic system by singular perturbation technique and show that the vanishing of obstructions for the perturbation is given precisely by the stability condition. This can be interpreted as an in nite dimensional analog of the equivalency between Geometric InvariantTheory and SymplecticReduction for moduli space of vector bundles.
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