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.

Let $𝒳\to S$ be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and $ℱ$ a $G$-bundle over $𝒳$ with connection along the fibres $𝒳\to S$. We construct a line bundle with connection $\left({ℒ}_{ℱ},{\nabla }_{ℱ}\right)$ on $S$ (also in cases when the connection on $ℱ$ has regular singularities). We discuss the resulting $\left({ℒ}_{ℱ},{\nabla }_{ℱ}\right)$ mainly in the case $G={ℂ}^{*}$. For instance when $S$ is the moduli space of line bundles with connection over a Riemann surface $X$, $𝒳=X×S$, and $ℱ$ is the Poincaré bundle over $𝒳$, we show that $\left({ℒ}_{ℱ},{\nabla }_{ℱ}\right)$ 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 = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.191/}
}
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Andres Rodriguez. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.191/

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