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.

Let 𝒳S be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and a G-bundle over 𝒳 with connection along the fibres 𝒳S. We construct a line bundle with connection ( , ) on S (also in cases when the connection on has regular singularities). We discuss the resulting ( , ) mainly in the case G= * . For instance when S is the moduli space of line bundles with connection over a Riemann surface X, 𝒳=X×S, and is the Poincaré bundle over 𝒳, we show that ( , ) provides a prequantization of S.

@article{AMBP_2004__11_2_181_0,
     author = {Andres Rodriguez},
     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 = {ambp.centre-mersenne.org/item/AMBP_2004__11_2_181_0/}
}
Andres Rodriguez. 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. https://ambp.centre-mersenne.org/item/AMBP_2004__11_2_181_0/

[1] P. Deligne Théorie de Hodge. III., Inst. Hautes Ètudes Sci. Publ. Math., Volume 44 (1974), pp. 5-77 | Article | Numdam | MR 498552 | Zbl 0237.14003