Let be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and a -bundle over with connection along the fibres . We construct a line bundle with connection on (also in cases when the connection on has regular singularities). We discuss the resulting mainly in the case . For instance when is the moduli space of line bundles with connection over a Riemann surface , , and is the Poincaré bundle over , we show that provides a prequantization of .
@article{AMBP_2004__11_2_181_0, author = {Rodriguez, Andres}, title = {Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces}, journal = {Annales Math\'ematiques Blaise Pascal}, pages = {181--186}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {11}, number = {2}, year = {2004}, doi = {10.5802/ambp.191}, mrnumber = {2109606}, zbl = {1078.53095}, language = {en}, url = {www.numdam.org/item/AMBP_2004__11_2_181_0/} }
Rodriguez, Andres. Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces. Annales Mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 181-186. doi : 10.5802/ambp.191. http://www.numdam.org/item/AMBP_2004__11_2_181_0/
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