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arXiv · 1611.00971

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

Arata Komyo·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 $\mathbb{P}^1$ and rank 2 (parabolic) Higgs bundle 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.

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Arata Komyo, Masa-Hiko Saito. 2016-11-03. Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces. https://doi.org/10.1215/21562261-2019-0016

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