Real Structures on Root Stacks and Parabolic Connections

Abstract

Let $D$ be a reduced effective strict normal crossing divisor on a smooth complex variety $X$, and let ${\mathfrak{X}}_D$ be an associated root stack over $\mathbb{C}$. Suppose that $X$ admits an anti-holomorphic involution (real structure) that keeps $D$ invariant. We show that the root stack ${\mathfrak{X}}_D$ 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 $X$.

27 pages, accepted for publication in Geometriae Dedicata