Annales Mathématiques
Blaise Pascal
no. 2
Notes on prequantization of moduli of G-bundles with connection on Riemann surfaces
Andres Rodriguez1
1 University of Chicago Department of Mathematics 5734 S. University Avenue Chicago, Illinois 60637 USA
Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 181-186.

Let 𝒳→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→S. We construct a line bundle with connection (ℒ ℱ ,∇ ℱ ) on S (also in cases when the connection on ℱ has regular singularities). We discuss the resulting (ℒ ℱ ,∇ ℱ ) 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 (ℒ ℱ ,∇ ℱ ) 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, Tome 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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