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.
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Acknowledgements
We would like to thank the anonymous referee for his/her careful reading of the manuscript and for helpful comments and suggestions that helped us clarify some points and to improve the exposition. This work was initiated during the first named author’s visit in the Department of Mathematics and Statistics of the Indian Institute of Science Education and Research Kolkata in December 2022. The second named author is partially supported by the DST INSPIRE Faculty Fellowship (Research Grant No.: DST/INSPIRE/04/2020/000649), Ministry of Science & Technology, Government of India.
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Chakraborty, S., Paul, A. Real structures on root stacks and parabolic connections. Geom Dedicata 218, 35 (2024). https://doi.org/10.1007/s10711-023-00880-1
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DOI: https://doi.org/10.1007/s10711-023-00880-1