Framed Parabolic sheaves on a trinion

TL;DR

This paper explores a toric structure on the moduli space of framed parabolic sheaves on a three-punctured sphere, extending to general Riemann surfaces through degenerations, with implications for geometric representation theory.

Contribution

It introduces a densely defined toric structure on moduli of framed parabolic sheaves, which degenerates to an actual toric structure, extending previous results to arbitrary Riemann surfaces.

Findings

Toric structure on moduli spaces for SU(n) and SL(n,C)

Degeneration of the structure to an actual toric form

Extension of results to arbitrary Riemann surfaces

Abstract

We consider for structure groups ${\rm SU}(n)\,\subset\, {\rm SL}(n,\mathbb C)$ a densely defined toric structure on the moduli of framed parabolic sheaves on a three-punctured sphere, which degenerates to an actual toric structure. In combination with previous degeneration results, these extend to similar moduli for arbitrary Riemann surfaces.