Logahoric Higgs torsors for a complex reductive group

Abstract

In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G, we introduce a notion of stability for logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors on a smooth algebraic curve X, where $$\mathcal {G}_{\varvec{\theta }}$$ is a parahoric group scheme on X. In the case when the group G is the general linear group $$\textrm{GL}_n$$ , we show that the stability condition of a parahoric torsor is equivalent to the stability of a parabolic bundle. A correspondence between semistable logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors and semistable equivariant logarithmic G-Higgs bundles allows us to construct the moduli space explicitly. This moduli space is shown to be equipped with an algebraic Poisson structure.