Journal of Symplectic Geometry

Volume 12 (2014)

Number 2

Removal of singularities and Gromov compactness for symplectic vortices

Pages: 257 – 311



Andreas Ott (Centre for Mathematical Sciences, University of Cambridge, United Kingdom)


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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