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

Rodriguez, Andres. "Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces." Annales mathématiques Blaise Pascal 11.2 (2004): 181-186. <http://eudml.org/doc/10504>.

@article{Rodriguez2004,
abstract = {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 $S$.},
affiliation = {University of Chicago Department of Mathematics 5734 S. University Avenue Chicago, Illinois 60637 USA},
author = {Rodriguez, Andres},
journal = {Annales mathématiques Blaise Pascal},
keywords = {line bundle; regular singularities; moduli space},
language = {eng},
month = {7},
number = {2},
pages = {181-186},
publisher = {Annales mathématiques Blaise Pascal},
title = {Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces},
url = {http://eudml.org/doc/10504},
volume = {11},
year = {2004},
}

TY - JOUR
AU - Rodriguez, Andres
TI - Notes on prequantization of moduli of $G$-bundles with connection on Riemann surfaces
JO - Annales mathématiques Blaise Pascal
DA - 2004/7//
PB - Annales mathématiques Blaise Pascal
VL - 11
IS - 2
SP - 181
EP - 186
AB - 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 $S$.
LA - eng
KW - line bundle; regular singularities; moduli space
UR - http://eudml.org/doc/10504
ER -