Torelli theorem for the moduli spaces of rank 2 quadratic pairs

TL;DR

This paper establishes a Torelli theorem for the moduli space of rank 2 quadratic pairs on a smooth projective complex curve, linking the geometry of the moduli space to the underlying curve.

Contribution

It proves a Torelli type theorem for the moduli space of rank 2 quadratic pairs, extending classical results to this new setting.

Findings

Torelli theorem holds for certain moduli spaces of quadratic pairs

Moduli space geometry encodes the curve's structure

Conditions under which the theorem applies are specified

Abstract

Let $X$ be a smooth projective complex curve. We prove that a Torelli type theorem holds, under certain conditions, for the moduli space of $\alpha$-polystable quadratic pairs on $X$ of rank 2.