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

Abstract

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 → Ad P ⊗ Ω X 1 . 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 → S l ( V ) of G , we consider principal Higgs bundles as triples ( E , q , φ ) , 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 φ : E a , b → L is a morphism of bundles, L being a line bundle and E a , b ≑ ( E ⊗ a ) ⊕ b a vector bundle depending on the Higgs field ϕ and on the principal bundle structure.