On symplectic vortex equations over a compact orbifold Riemann surface

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack. After that we define symplectic vortex equations over a compact orbifold Riemann surface. We also discuss the moduli space of solutions to the equations for linear actions of the circle group on the complex plane.

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The author would like to thank the Max-Planck-Institut für Mathematik in Bonn for providing financial support and excellent environment during my stay. He would also like to thank Andreas Ott and Nuno Miguel Romão for valuable comments and discussions.

Received 25 October 2012

Accepted 26 April 2015

Published 28 November 2017