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Real Structures on Root Stacks and Parabolic Connections

Author:
Sujoy Chakraborty, Arjun Paul
Keyword:
Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)
journal:
--
date:
2023-07-02 16:00:00
Abstract
Let $D$ be a reduced effective strict normal crossing divisor on a smooth complex variety $X$, and let $\mathfrak{X}_D$ be the 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 $X$.
PDF: Real Structures on Root Stacks and Parabolic Connections.pdf
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