Kyoto Journal of Mathematics

Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces

Arata Komyo and Masa-Hiko Saito

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Abstract

In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on P1 and rank 2 (parabolic) Higgs bundles on P1. Then we obtain explicit descriptions of Zariski-open sets of the moduli space of the parabolic connections and the moduli space of the Higgs bundles. For n=5, we can give global descriptions of the moduli spaces in detail.

Article information

Source
Kyoto J. Math., Volume 59, Number 3 (2019), 515-552.

Dates
Received: 23 January 2017
Revised: 2 April 2017
Accepted: 6 April 2017
First available in Project Euclid: 16 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1563242599

Digital Object Identifier
doi:10.1215/21562261-2019-0016

Mathematical Reviews number (MathSciNet)
MR3990176

Subjects
Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 34M55: Painlevé and other special equations; classification, hierarchies; 32G34: Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation) [See also 34Mxx]

Keywords
parabolic connection parabolic Higgs bundle apparent singularity

Citation

Komyo, Arata; Saito, Masa-Hiko. Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces. Kyoto J. Math. 59 (2019), no. 3, 515--552. doi:10.1215/21562261-2019-0016. https://projecteuclid.org/euclid.kjm/1563242599


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References

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