A chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}$-twisted rank 2 constrained framed Hitchin pairs on a smooth curve

TL;DR

This paper establishes a surjective relationship between chains of $ ext{C}^*$-flips in moduli spaces of twisted Hitchin pairs and framed modules on a smooth projective curve, revealing structural connections.

Contribution

It constructs a surjective diagram linking $ ext{C}^*$-flip chains of twisted Hitchin pairs to those of framed modules, providing new insights into their geometric relations.

Findings

Established a surjective diagram between moduli space chains

Connected twisted Hitchin pairs with framed modules

Revealed structural relationships in moduli space transformations

Abstract

Let $X$ be a smooth complex projective curve. We prove that there exists a surjective commutative forgetful diagram from the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}_{X}$-twisted rank 2 constrained framed Hitchin pairs on $X$ to the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of rank 2 framed modules on $X$.