Moduli of vortices and Grassmann manifolds

DOI10.1007/S00220-013-1704-3zbMATH Open1274.14040arXiv1012.4023OpenAlexW1965164312MaRDI QIDQ2376973

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Publication date: 26 June 2013

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1012.4023

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