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research
Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface
Authors
Axelrod S.
Guillemin V.
Rukmini Dey
Woodhouse N. M. J.
Publication date
19 December 2006
Publisher
'AIP Publishing'
Doi
Cite
View
on
arXiv
Abstract
The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures
Ω
Ψ
0
\Omega_{\Psi_0}
Ω
Ψ
0
​
​
on the moduli space, parametrised by
Ψ
0
\Psi_0
Ψ
0
​
, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles
P
Ψ
0
{\mathcal P}_{\Psi_0}
P
Ψ
0
​
​
on the moduli space whose curvature is proportional to the symplectic forms
Ω
Ψ
0
\Omega_{\Psi_0}
Ω
Ψ
0
​
​
.Comment: 8 page
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Last time updated on 02/01/2020