Twistor deformation of rank one local systems

TL;DR

This paper characterizes the twistor deformation of rank one local systems on compact Kähler manifolds, connecting it with twistor modules and the Picard variety, using an elementary approach.

Contribution

It provides an elementary proof describing the twistor deformation of rank one local systems, linking it to the moduli space and Picard variety.

Findings

Explicit description of twistor deformation for rank one local systems

Connection between twistor modules and Picard variety

Elementary proof technique for deformation analysis

Abstract

We determine the twistor deformation of rank one local systems on compact Kaehler manifolds which correspond to smooth twistor modules of rank one in the sense of C. Sabbah. Our proof is rather elementary, and uses a natural description of the moduli space of rank one local systems together with the canonical morphism to the Picard variety. The corresponding assertion for smooth twistor modules of rank one follows from the theory of C. Simpson and has been known to the specialists, according to T. Mochizuki.