The Determinant of Cohomology and Moduli of $\lambda$-Connections

TL;DR

This paper explores the structure of the Hodge-Deligne moduli space of λ-connections on smooth projective curves, revealing its duality relationship with the Atiyah algebroid of the determinant of cohomology line bundle.

Contribution

It demonstrates a duality interpretation of the Hodge-Deligne moduli space as the dual of the Atiyah algebroid related to the determinant of cohomology.

Findings

Hodge-Deligne moduli space can be understood via duality with Atiyah algebroid.

The structure of λ-connections is linked to the geometry of determinant line bundles.

Provides a new perspective on the moduli space of λ-connections.

Abstract

We exhibit how the Hodge-Deligne moduli space of $\lambda$-connections over a smooth projective curve, for stable bundles with fixed determinant, can be understood as the dual of the Atiyah algebroid of the determinant of cohomology line bundle.