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arXiv · 1903.03555

The locus of the representation of logarithmic connections by Fuchsian equations

Péter Ivanics
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Abstract

The generic element of the moduli space of logarithmic connections with parabolic points on holomorphic vector bundle over the Riemann sphere can be represented by a Fuchsian equation with some singularities and some apparent singularities. We analyze the case of rank $3$ vector bundle which leads to third order Fuchsian equation. We find coordinates on an open subset of the moduli space and we construct a non-trivial part of the moduli space by blowing up along a variety in a special case.

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Péter Ivanics. 2019-03-08. The locus of the representation of logarithmic connections by Fuchsian equations. https://arxiv.org/abs/1903.03555

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