Abelian Vortices with Singularities

X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
Comment: 23 pages -->
Druh dokumentu: Working Paper
Přístupová URL adresa: http://arxiv.org/abs/1207.0863
Přírůstkové číslo: edsarx.1207.0863
Autor: Baptista, J. M., Biswas, Indranil
Rok vydání: 2012
Předmět:
Zdroj: Diff. Geom. Appl. 31: 725-745, 2013
Druh dokumentu: Working Paper
Popis: Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
Comment: 23 pages
Databáze: arXiv
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