Moduli of vortices and Grassmann manifolds

Details Moduli of vortices and Grassmann manifolds Moduli of vortices and Grassmann manifolds

2010-12-17

arxiv.org/abs/1012.4023v1

Mathematics

Algebraic Geometry

27 pages, LaTeX

Scientific paper

We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli spaces embed canonically into certain Grassmann manifolds, and thus obtain natural Kaehler metrics of Fubini-Study type; these spaces are smooth at least in the local case r=n. For abelian local vortices we prove that, if a certain "quantization" condition is satisfied, the embedding can be chosen in such a way that the induced Fubini-Study structure realizes the Kaehler class of the usual L^2 metric of gauged vortices. We also give a detailed description of the moduli spaces in the nonabelian local case.

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