Unfolding of the unramified irregular singular generalized isomonodromic deformation (Q2335845)

The aim of the paper is to produce a tool toward understanding the confluence phenomena connecting the regular singular isomonodromic deformation and the irregular singular generalized isomonodromic deformation. An example in this direction is the case of connections on \(\mathbb{P}^1\), when the regular singular isomonodromic deformation is the Schlesinger equation and the unramified irregular singular generalized isomonodromic deformation is the Jimbo-Miwa-Ueno equation. To this end the author introduces an unfolded moduli space of connections, which is an algebraic relative moduli space of connections on complex smooth projective curves, whose generic fiber is a moduli space of regular singular connections and whose special fiber is a moduli space of unramified irregular singular connections. On the moduli space of unramified irregular singular connections, there is a subbundle of the tangent bundle defining the generalized isomonodromic deformation produced by the Jimbo-Miwa-Ueno theory. On an analytic open subset of the unfolded moduli space of connections, a non-canonical lift of this subbundle is constructed, which is called an unfolding of the unramified irregular singular generalized isomonodromic deformation. This construction of an unfolding is not compatible with the asymptotic property in the unfolding theory established by Hurtubise, Lambert and Rousseau which gives unfolded Stokes matrices for an unfolded linear differential equation in a general framework.