Abstract
We compute the effective good divisibility of a rational homogeneous variety, extending an earlier result for complex Grassmannians by Naldi and Occhetta. Non-existence of nonconstant morphisms to rational homogeneous varieties of classical Lie type are obtained as applications.
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Acknowledgements
The authors thank Pierre-Emmanuel Chaput, Haibao Duan, Jianxun Hu, Xiaowen Hu, Hua-Zhong Ke, Naichung Conan Leung, Leonardo Constantin Mihalcea, Lei Song and Heng Xie for helpful discussions. The authors are extremely grateful to the anomynous referee for the very careful reading and the quite valuable comments. C. Li is supported by NSFC Grants 12271529 and 11831017, and Guangdong Introducing Innovative and Enterpreneurial Teams No. 2017ZT07X355.
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While this manuscript was almost finished, Muñoz, Occhetta and Solá Conde posted a preprint [17] independently proving Theorems 1.1 and 1.2 for rational homogeneous varieties of classical type. Our proof is completely different from theirs, and our main results hold for all Lie types.
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Hu, H., Li, C. & Liu, Z. Effective good divisibility of rational homogeneous varieties. Math. Z. 305, 52 (2023). https://doi.org/10.1007/s00209-023-03383-7
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DOI: https://doi.org/10.1007/s00209-023-03383-7