Moduli of regular singular parabolic connections of spectral type on smooth projective curves

TL;DR

This paper constructs and analyzes a moduli space of stable regular singular parabolic connections on smooth projective curves, demonstrating its smoothness, symplectic structure, and the geometric Painlevé property of associated isomonodromic deformations.

Contribution

It introduces a new moduli space for spectral type parabolic connections, proves its smoothness and symplectic structure, and establishes the geometric Painlevé property for isomonodromic deformations.

Findings

Moduli space is smooth and symplectic.

Isomonodromic deformations satisfy the geometric Painlevé property.

Provides a framework for studying regular singular parabolic connections.

Abstract

We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we define the isomonodromic deformation on this moduli space and prove the geometric Painlev\'e property of the isomonodromic deformation.