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

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 -> AdP circle times ohm(1)(X). 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 rho : G -> SI(V) of G, we consider principal Higgs bundles as triples (E, q, phi), where E is a vector bundle with rk(E) = dim V over the normalization X of X, q is a parabolic structure on E and phi : E-a,E-b -> L is a morphism of bundles, L being a line bundle and E-a,E-b double dagger (E-circle times a)(circle times b) a vector bundle depending on the Higgs field phi, and on the principal bundle structure. (C) 2016 Elsevier B.V. All rights reserved.