The Moduli Space of Flat G-bundles on a Compact Hyper-kähler Manifold
نویسندگان
چکیده
where Hom(π1(X), G) denotes the space of all group homomorphisms from the fundamental group π1(X) into G, and G acts on this space by conjugation. Let φ : π1(X) → G be a homomorphism, and let [φ] denote the corresponding point of LocG(X). Note that φ defines a π1(X)-module structure on g via the adjoint representation of G. Let us denote this π1(X)-module by gφ, and let Eφ denote the associated flat vector bundle on X. It is well known (see, e.g., [Hi]) that if [φ] is a smooth point of LocG(X), then there is a natural identification of the tangent space T[φ] LocG(X) ∼= H 1 DR(X,Eφ). (1.1)
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