1012.4023 (Indranil Biswas et al.)

Moduli of vortices and Grassmann manifolds    [PDF]

Indranil Biswas, Nuno M. Romão

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.

View original: http://arxiv.org/abs/1012.4023