Real Structures on Root Stacks and Parabolic Connections

2023/07/03 by Sujoy Chakraborty, Chakraborty, Sujoy, Arjun Paul +1
Computer Science · #14A21 #14D23 #14H60 #53B15 #53C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.2307.00796

openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be a reduced effective strict normal crossing divisor on a smooth complex variety X, and let \mathfrakX_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 \mathfrakX_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.

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