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}, zbl = {1078.53095}, mrnumber = {2109606}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ambp.191/} }
TY - JOUR AU - Rodriguez, Andres TI - Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces JO - Annales mathématiques Blaise Pascal PY - 2004 SP - 181 EP - 186 VL - 11 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.191/ DO - 10.5802/ambp.191 LA - en ID - AMBP_2004__11_2_181_0 ER -
%0 Journal Article %A Rodriguez, Andres %T Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces %J Annales mathématiques Blaise Pascal %D 2004 %P 181-186 %V 11 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.191/ %R 10.5802/ambp.191 %G en %F 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, Volume 11 (2004) no. 2, pp. 181-186. doi : 10.5802/ambp.191. http://www.numdam.org/articles/10.5802/ambp.191/