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Submanifolds of ℙn(l) with Splitting Tangent Sequence

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Abstract

Let l be a line in a projective space ℙn. We consider the blowing up ℙn(l) of ℙn along l. Assume that X is a smooth closed subvariety of ℙn. If the strict transform of X in ℙn(l) has a splitting tangent sequence and dim X is at least 2, then X is a linear subspace of ℙn.

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Acknowledgements

The author would like to thank Baohua Fu for many inspiring discussions and suggestions, especially for his help to introduce and explain this problem to the author. The author is very grateful to the referee who helps to improve the exposition of this article.

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Authors and Affiliations

  1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, P. R. China

    Duo Li

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  1. Duo Li
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Correspondence to Duo Li.

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Supported by National Natural Science Foundation of China (Grant No. 12001547) and Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515110907)

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Li, D. Submanifolds of ℙn(l) with Splitting Tangent Sequence. Acta. Math. Sin.-English Ser. 38, 397–405 (2022). https://doi.org/10.1007/s10114-022-1047-0

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  • DOI: https://doi.org/10.1007/s10114-022-1047-0

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