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Singularities and Kodaira dimension of the moduli space of flat Hermitian-Yang-Mills connections. (English) Zbl 0652.32017
The author studies the moduli space of stable holomorphic vector bundles E over a compact Kähler manifold M with \(c_ 2(End E)=0\). He shows that if two (0,1)-forms with values in End E are harmonic relative to the Hermitian-Yang-Mills metric then so is their product. As a consequence, he obtains the fact that no higher order obstructions exist in the deformation theory of E. Then he proves that the singularities of the moduli space are quadratic algebraic, and that if M is algebraic then the Kodaira dimension of the moduli space cannot be maximal.
Reviewer: I.Vaisman

MSC:
32G99 Deformations of analytic structures
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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