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Parabolic Higgs bundles on projecitive line, quiver varieties and Deligne-Simpson problem (2101.01913v2)
Published 6 Jan 2021 in math.AG
Abstract: We establish an isomorphism between the moduli space of parabolic Higgs bundles on the projective line and quiver variety of star-shaped quiver. As applications, we can solve the nilpotent case of the Deligne-Simpson problem in a geometrical way; and we can show that there is an algebraically completely integrable system structure on the moduli space as well as quiver variety we concerned.
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