Flat connections and geometric quantization. Hitchin, N. J. Communications in Mathematical Physics, 131(2):347–380, July, 1990.
Flat connections and geometric quantization [link]Paper  doi  abstract   bibtex   
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 Teichmϋller 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 Cech techniques are used.
@article{hitchin_flat_1990,
	title = {Flat connections and geometric quantization},
	volume = {131},
	issn = {0010-3616, 1432-0916},
	url = {http://link.springer.com/10.1007/BF02161419},
	doi = {10.1007/BF02161419},
	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 Teichmϋller 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 Cech techniques are used.},
	language = {en},
	number = {2},
	urldate = {2019-03-10},
	journal = {Communications in Mathematical Physics},
	author = {Hitchin, N. J.},
	month = jul,
	year = {1990},
	pages = {347--380}
}

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