arXiv subjects
Publications and source records attributed to Takafumi Matsumoto.
An $A^{(1)*}_2$-surface is a space of initial conditions of certain difference Painlevé equations. $A^{(1)*}_2$-surfaces are realized as the moduli spaces of parabolic logarithmic connections. In this paper, we realize the symmetry of $A^{(1)*}_2$-surfaces as transformations of parabolic 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.
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.