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Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

Rukmini Dey
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Abstract

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact Kähler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, Kähler) structures $Ω_{Ψ_0}$ on the moduli space, parametrised by $Ψ_0$, 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 ${\mathcal P}_{Ψ_0} $on the moduli space whose curvature is proportional to the symplectic forms $Ω_{Ψ_0}$.

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BibTeXRIS

Rukmini Dey. 2006-12-19. Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface. https://doi.org/10.1063/1.2352858

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