Abstract
The n th symmetric product of a Riemann surface carries a natural family of Kähler forms, arising from its interpretation as a moduli space of abelian vortices. We give a new proof of a formula of Manton–Nasir [10] for the cohomology classes of these forms. Further, we show how these ideas generalise to families of Riemann surfaces.
These results help to clarify a conjecture of D. Salamon [13] on the relationship between Seiberg–Witten theory on 3–manifolds fibred over the circle and symplectic Floer homology.
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Communicated by N.A. Nekrasov
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Perutz, T. Symplectic Fibrations and the Abelian Vortex Equations. Commun. Math. Phys. 278, 289–306 (2008). https://doi.org/10.1007/s00220-007-0402-4
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DOI: https://doi.org/10.1007/s00220-007-0402-4