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 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.

DOI: 10.5802/ambp.191
Andres Rodriguez 1

1 University of Chicago Department of Mathematics 5734 S. University Avenue Chicago, Illinois 60637 USA
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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/

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

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