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Transactions of the American Mathematical Society

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Classification of Mukai pairs with dimension $ 4$ and rank $ 2$


Author: Akihiro Kanemitsu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14J35, 14J40, 14J45, 14J60
DOI: https://doi.org/10.1090/tran/7824
Published electronically: June 17, 2019
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Abstract: We give the complete classification of Mukai pairs of dimension $ 4$ and rank $ 2$ with Picard number one, that is, pairs $ (X,\mathcal {E})$ where $ X$ is a Fano $ 4$-fold with Picard number one, and $ \mathcal {E}$ is an ample vector bundle of rank 2 on $ X$ with $ c_1(X) = c_1(\mathcal {E})$. Equivalently, the present paper completes the classification of ruled Fano $ 5$-folds with index two, which was partially done by C. Novelli and G. Occhetta in 2007.


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Additional Information

Akihiro Kanemitsu
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
Email: kanemitu@math.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/tran/7824
Keywords: Fano manifold, vector bundle, Mukai pair
Received by editor(s): October 9, 2018
Received by editor(s) in revised form: February 1, 2019
Published electronically: June 17, 2019
Additional Notes: The author is a JSPS Research Fellow and was supported by the Grant-in-Aid for JSPS fellows (JSPS KAKENHI Grants Number 15J07608, 18J00681). This work was supported by the Program for Leading Graduate Schools, MEXT, Japan.
Article copyright: © Copyright 2019 American Mathematical Society