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arXiv · 1410.6467

Hyperpolygons and Hitchin systems

Jonathan Fisher·Steven Rayan
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Abstract

We study the hyperkähler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperkähler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these spaces for all ranks. Building on a natural analogy between hyperpolygons and parabolic Higgs bundles, we identify hyperpolygon spaces with certain degenerate Hitchin systems, and use this to establish their complete integrability, for ranks up to and including 3.

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Jonathan Fisher, Steven Rayan. 2014-10-23. Hyperpolygons and Hitchin systems. https://doi.org/10.1093/imrn%2Frnv172

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