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Takafumi Matsumoto

Publications and source records attributed to Takafumi Matsumoto.

4 recordsLinked to original sources
arXiv2026

Moduli spaces of logarithmic connections associated with difference Painlevé equations of type $E^{(1)}_n$

In this paper, we provide an explicit correspondence between moduli spaces of parabolic logarithmic connections on the projective line with spectral type $(2^2,1^4,1^4)$ and $(3^2, 2^3, 1^6)$, and the spaces of initial conditions for difference Painlevé equations with symmetry of type $E^{(1)}_7$ and $E^{(1)}_8$, respectively. Furthermore, we realize the extended affine Weyl group symmetries of the space of initial conditions in terms of connections.

math.AG↗
arXiv2024

Birational description of moduli spaces of rank 2 logarithmic connections

In this paper, we provide an explicit description of the Zariski-open subset of the moduli space of rank 2 parabolic logarithmic connections in the case $g\geq 2$. Our approach is to analyze the underlying parabolic bundles and the apparent singularities of the parabolic connections. We prove that a Zariski-open subset of the product of a projective space and the moduli space of parabolic bundles gives a Darboux coordinate for the moduli space of parabolic connections.

math.AG↗
arXiv2024

Moduli space of rank three logarithmic connections on the projective line with three poles

In this paper, we describe the moduli space of rank three parabolic logarithmic connections on the projective line with three poles for any local exponents. In particular, we show that the family of moduli spaces of rank three parabolic $ϕ$-connections on the projective line with three poles is isomorphic to the family of $A^{(1)*}_2$-surfaces in Sakai's classification of Painlevé equations. Through this description, we investigate the relation between the apparent singularities and underlying parabolic bundles.

math.AG↗