Torelli theorem for the parabolic Deligne-Hitchin moduli space

TL;DR

This paper demonstrates that the isomorphism class of the parabolic Deligne-Hitchin moduli space uniquely determines the underlying curve and its parabolic points, establishing a Torelli-type theorem.

Contribution

It proves a Torelli theorem for the parabolic Deligne-Hitchin moduli space, linking its isomorphism class to the underlying geometric data.

Findings

The isomorphism class of the moduli space determines the curve and parabolic points.

Establishes a Torelli-type result for parabolic Deligne-Hitchin moduli spaces.

Provides a new tool for reconstructing curves from moduli space data.

Abstract

We prove that, given the isomorphism class of the parabolic Deligne-Hitchin moduli space over a smooth projective curve, we can recover the isomorphism class of the curve and the parabolic points.