## Kyoto Journal of Mathematics

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

#### Abstract

In this paper, we investigate the apparent singularities and the dual parameters of rank $2$ parabolic connections on $\mathbb{P}^{1}$ and rank $2$ (parabolic) Higgs bundles on $\mathbb{P}^{1}$. 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
Revised: 2 April 2017
Accepted: 6 April 2017
First available in Project Euclid: 16 July 2019

https://projecteuclid.org/euclid.kjm/1563242599

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

Mathematical Reviews number (MathSciNet)
MR3990176

#### 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

#### References

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