Explicit Determination of the Picard Group of Moduli Spaces of Semistable G-Bundles on Curves
نویسندگان
چکیده
Let G be a connected, simply-connected, simple affine algebraic group and Cg be a smooth irreducible projective curve of any genus g ≥ 1 over C. Denote by MCg (G) the moduli space of semistable principal G-bundles on Cg. Let Pic(MCg (G)) be the Picard group of MCg (G) and let X be the infinite Grassmannian of the affine Kac-Moody group associated to G. It is known that Pic(X) ≃ Z and is generated by a homogenous line bundle Lχ0. Also, as proved by Kumar-Narasimhan [KN], there exists a canonical injective group homomorphism
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