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

A principal Higgs bundle (P,ϕ) over a singular curve X is a pair consisting of a principal bundle P and a morphism ϕ:X→AdP⊗ΩX1. We construct the moduli space of principal Higgs G-bundles over an irreducible singular curve X using the theory of decorated vector bundles. More precisely, given a faithful representation ρ:G→Sl(V) of G, we consider principal Higgs bundles as triples (E,q,φ), where E is a vector bundle with rk(E)=dimV over the normalization X˜ of X, q is a parabolic structure on E and φ:Ea,b→L is a morphism of bundles, L being a line bundle and Ea,b≑(E⊗a)⊕b a vector bundle depending on the Higgs field ϕ and on the principal bundle structure.