Real Structures on Root Stacks and Parabolic Connections
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911758773387264 |
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| author | Chakraborty, Sujoy Paul, Arjun |
| author_facet | Chakraborty, Sujoy Paul, Arjun |
| contents | 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 $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00796 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real Structures on Root Stacks and Parabolic Connections Chakraborty, Sujoy Paul, Arjun Algebraic Geometry 14D23, 14H60, 53B15, 53C05, 14A21 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 $X$. |
| title | Real Structures on Root Stacks and Parabolic Connections |
| topic | Algebraic Geometry 14D23, 14H60, 53B15, 53C05, 14A21 |
| url | https://arxiv.org/abs/2307.00796 |