Moduli of vortices and Grassmann manifolds

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.

22 pages, LaTeX. Final version: last section removed, typos corrected, two references added; to appear in Commun. Math. Phys

References in corpus (5)

• Solitons in the Higgs phase -- the moduli matrix approach --
• Quantum Vortex Strings: A Review
• On the L^2-metric of vortex moduli spaces
• Non-abelian vortices on compact Riemann surfaces
• Vortices and Jacobian varieties

Cited by in corpus (6)

• Vertices, Vortices & Interacting Surface Operators
• Twisted Indices of 3d $\mathcal{N}=4$ Gauge Theories and Enumerative Geometry of Quasi-Maps
• Vortex counting and the quantum Hall effect
• Pairs of pants, Pochhammer curves and $L^2$-invariants
• Quot schemes and Ricci semipositivity
• Bergman kernel on Riemann surfaces and Kaehler metric on symmetric products