Vortices and Jacobian varieties
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Publication:533436
DOI10.1016/J.GEOMPHYS.2011.02.017zbMATH Open1216.81107arXiv1010.0644OpenAlexW1593325590MaRDI QIDQ533436
Author name not available (Why is that?)
Publication date: 3 May 2011
Published in: (Search for Journal in Brave)
Abstract: We investigate the geometry of the moduli space of N-vortices on line bundles over a closed Riemann surface of genus g > 1, in the little explored situation where 1 =< N < g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of the surface. For N = 1, we show that the metric on the moduli space converges to a natural Bergman metric on the Riemann surface. When N > 1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel-Jacobi map at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics.
Full work available at URL: https://arxiv.org/abs/1010.0644
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