Real structures on root stacks and parabolic connections

Let D be a reduced effective strict normal crossing divisor on a smooth complex variety X , and let 𝔛_D be the associated root stack over ℂ . Suppose that X admits an anti-holomorphic involution (real structure) that keeps D invariant. We show that the root stack 𝔛_D naturally admits a real structure compatible with X . We also establish an equivalence of categories between the category of real logarithmic connections on this root stack and the category of real parabolic connections on X .