A compactification of the moduli space of principal Higgs bundles over singular curves (Q335841)

The authors consider principal Higgs bundles over singular curves and construct their moduli spaces. A principal Higgs bundle \((P,\phi)\) over a singular curve \(X\) is a pair consisting of a principal bundle \(P\) and a morphism \(\phi:X\longrightarrow \mathrm{Ad}P\otimes X\). The authors construct the moduli space of principal Higgs \(G\)-bundles over an irreducible singular curve \(X\) using the theory of decorated vector bundles.NEWLINENEWLINEMore precisely, given a faithful representation \(\rho:G\longrightarrow \mathrm{SL}(V)\) of \(G\), they consider principal Higgs bundles as triples \((E,q,\phi)\) where \(E\) is a vector bundle with \(\mathrm{rk}{E}=\dim V\) over the normalization \(\widetilde{X}\) of \(X\), \(q\) is a parabolic structure on \(E\) and \(\phi:E_{a,b}\longrightarrow L\) is a morphism of bundles, being \(L\) a line bundle and \(E_{a,b}\doteqdot (E^{\otimes a})^{\oplus b}\) a vector bundle depending on the Higgs field \(\phi\) and on the principal bundle structure. Moreover they show that this moduli space for suitable integers \(a,b\) is related to the space of framed modules.