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Flat connections and geometric quantization

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Abstract

Using the space of holomorphic symmetric tensors on the moduli space of stable bundles over a Riemann surface we construct a projectively flat connection on a vector bundle over Teichmüller space. The fibre of the vector bundle consists of the global sections of a power of the determinant bundle on the moduli space. Both Dolbeault and Čech techniques are used.

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Communicated N. Yu. Reshetikhin

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Hitchin, N.J. Flat connections and geometric quantization. Commun.Math. Phys. 131, 347–380 (1990). https://doi.org/10.1007/BF02161419

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