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June 2014 Removal of singularities and Gromov compactness for symplectic vortices
Andreas Ott
J. Symplectic Geom. 12(2): 257-311 (June 2014).


We prove that the moduli space of gauge equivalence classes of symplectic vortices with uniformly bounded energy in a compact Hamiltonian manifold admits a Gromov compactification by polystable vortices. This extends results of Mundet i Riera for circle actions to the case of arbitrary compact Lie groups. Our argument relies on an a priori estimate for vortices that allows us to apply techniques used by McDuff and Salamon in their proof of Gromov compactness for pseudoholomorphic curves. As an intermediate result we prove a removable singularity theorem for symplectic vortices.


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Andreas Ott. "Removal of singularities and Gromov compactness for symplectic vortices." J. Symplectic Geom. 12 (2) 257 - 311, June 2014.


Published: June 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1360.53080
MathSciNet: MR3210578

Rights: Copyright © 2014 International Press of Boston


Vol.12 • No. 2 • June 2014
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