Moduli space of parabolic $\Lambda$-modules over a curve

TL;DR

This paper introduces the concept of parabolic $ ext{Lambda}$-modules over a curve, constructs their moduli space, and applies this to develop the parabolic Hodge moduli space for parabolic $ ext{lambda}$-connections, extending Simpson's framework.

Contribution

It extends Simpson's moduli space construction to include parabolic $ ext{Lambda}$-modules and develops the parabolic Hodge moduli space for $ ext{lambda}$-connections.

Findings

Constructed the moduli space of parabolic $ ext{Lambda}$-modules.

Developed the parabolic Hodge moduli space for $ ext{lambda}$-connections.

Unified various special cases like Higgs bundles and connections.

Abstract

Simpson, in 1994, introduced the notion of $\Lambda$-modules and constructed the corresponding moduli space, where $\Lambda$ is a sheaf of rings of differential operators. Higgs bundles, connections and $\lambda$-connections (as defined by Delgine) are particular cases of $\Lambda$-modules. In this article the concept of parabolic $\Lambda$-modules over a curve is introduced and their moduli space is built. As an application, we construct the parabolic Hodge moduli space parameterizing parabolic $\lambda$-connections.