On moduli spaces of Hitchin pairs
Indranil Biswas, Peter B. Gothen, Marina Logares

TL;DR
This paper investigates the geometric structure of moduli spaces of Hitchin pairs on Riemann surfaces, establishing conditions for irreducibility and demonstrating that these moduli spaces uniquely identify the underlying surface.
Contribution
It proves irreducibility of certain Hitchin moduli spaces and shows they uniquely determine the Riemann surface, linking geometric properties to surface classification.
Findings
Proved irreducibility of moduli spaces under specific conditions
Demonstrated the moduli space uniquely determines the Riemann surface
Established numerical conditions for the main results
Abstract
Let be a compact Riemann surface of genus at--least two. Fix a holomorphic line bundle over . Let be the moduli space of Hitchin pairs over of rank and fixed determinant of degree . We prove that, for some numerical conditions, is irreducible, and that the isomorphism class of the variety uniquely determines the isomorphism class of the Riemann surface .
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