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Relative Bott–Samelson Varieties

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Abstract

We prove that, defined with respect to versal flags, the product of two relative Bott–Samelson varieties over a flag bundle is a resolution of singularities of a relative Richardson variety. This result generalizes Brion’s resolution of singularities of Richardson varieties to the relative setting. As an application, this gives a resolution of singularities, with a modular interpretation, for the Brill–Noether variety with imposed ramification on twice-marked elliptic curves.

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Acknowledgements

The author would like to thank Melody Chan for suggesting the problem and guidance throughout. The author extends gratitude to Dan Abramovich, Shamil Asgarli, and Giovanni Inchiostro for their insightful discussions, and to the referees for their meticulous reading and thoughtful comments.

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  1. Department of Mathematics, Brown University, Providence, RI, USA

    Shiyue Li

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  1. Shiyue Li
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Li, S. Relative Bott–Samelson Varieties. La Matematica 2, 420–437 (2023). https://doi.org/10.1007/s44007-023-00054-1

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  • DOI: https://doi.org/10.1007/s44007-023-00054-1

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