1 April 2017 Linear differential equations on the Riemann sphere and representations of quivers
Kazuki Hiroe
Duke Math. J. 166(5): 855-935 (1 April 2017). DOI: 10.1215/00127094-3769640


Our interest in this article is a generalization of the additive Deligne–Simpson problem, which was originally defined for Fuchsian differential equations on the Riemann sphere. We extend this problem to differential equations having an arbitrary number of unramified irregular singular points, and we determine the existence of solutions of the generalized additive Deligne–Simpson problems. Moreover, we apply this result to the geometry of the moduli spaces of stable meromorphic connections of trivial bundles on the Riemann sphere (namely, open embedding of the moduli spaces into quiver varieties and the nonemptiness condition of the moduli spaces). Furthermore, we detail the connectedness of the moduli spaces.


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Kazuki Hiroe. "Linear differential equations on the Riemann sphere and representations of quivers." Duke Math. J. 166 (5) 855 - 935, 1 April 2017. https://doi.org/10.1215/00127094-3769640


Received: 24 December 2014; Revised: 24 June 2016; Published: 1 April 2017
First available in Project Euclid: 12 November 2016

zbMATH: 1368.16018
MathSciNet: MR3626566
Digital Object Identifier: 10.1215/00127094-3769640

Primary: 16G20
Secondary: 34M25 , 34M56

Keywords: additive Deligne–Simpson problem , linear ODE with irregular singular points , middle convolution , moduli spaces of meromorphic connections , representations of quivers

Rights: Copyright © 2017 Duke University Press


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Vol.166 • No. 5 • 1 April 2017
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