Unfolding of the unramified irregular singular generalized isomonodromic deformation

TL;DR

This paper introduces an algebraic unfolded moduli space of connections that interpolates between regular and unramified irregular singular connections, and constructs a non-canonical lift of the isomonodromic deformation within this space.

Contribution

It presents a novel algebraic framework for unfolding unramified irregular singular connections and constructs a non-canonical lift of the isomonodromic deformation.

Findings

Constructed an unfolded moduli space of connections.

Defined a non-canonical lift of the isomonodromic deformation.

The construction is not compatible with existing asymptotic unfolding theories.

Abstract

We introduce 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, we construct a non-canonical lift of this subbundle, which we call an unfolding of the unramified irregular singular generalized isomonodromic deformation. Our construction of an unfolding of the unramified irregular singular generalized isomonodromic deformation 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.