Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces

Rodriguez, Andres

Annales mathématiques Blaise Pascal, Tome 11 (2004), p. 181-186 / Harvested from Numdam

Résumé

Let $\mathcal{X}\rightarrow S$ be a smooth proper family of complex curves (i.e. family of Riemann surfaces), and $\mathcal{F}$ a $G$-bundle over $\mathcal{X}$ with connection along the fibres $\mathcal{X}\rightarrow S$. We construct a line bundle with connection $(\mathcal{L}_{\mathcal{F}},\nabla _{\mathcal{F}})$ on $S$ (also in cases when the connection on $\mathcal{F}$ has regular singularities). We discuss the resulting $(\mathcal{L}_{\mathcal{F}},\nabla _{\mathcal{F}})$ mainly in the case $G=\mathbb{C}^*$. For instance when $S$ is the moduli space of line bundles with connection over a Riemann surface $X$, $\mathcal{X}= X \times S$, and $\mathcal{F}$ is the Poincaré bundle over $\mathcal{X}$, we show that $(\mathcal{L}_{\mathcal{F}},\nabla _{\mathcal{F}})$ provides a prequantization of $S$.

Détail

Publié le : 2004-01-01

MR 2109606 | Zbl 1078.53095

DOI : https://doi.org/10.5802/ambp.191

Bibliographie

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