Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Surfaces on the Severi line in positive characteristic
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by Yi Gu, Xiaotao Sun and Mingshuo Zhou PDF
Trans. Amer. Math. Soc. 375 (2022), 6015-6041 Request permission

Abstract:

Let $\mathbf {k}$ be an algebraically closed field, a minimal surface $X$ over $\mathbf {k}$ of maximal Albanese dimension is called on the Severi line if the ‘Severi equality’: $K^2_X=4\chi (\mathcal {O}_X)$ holds. We prove that $X$ is on the Severi line if and only if its canonical model $X_{\mathrm {can}}$ admits a flat double cover over an Abelian surface.
References
Additional Information
  • Yi Gu
  • Affiliation: School of Mathematical Sciences, Soochow University, Suzhou 215006, People’s Republic of China
  • ORCID: 0000-0003-1474-7896
  • Email: sudaguyi2017@suda.edu
  • Xiaotao Sun
  • Affiliation: Center of Applied Mathematics, School of Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
  • Email: xiaotaosun@tju.edu.cn
  • Mingshuo Zhou
  • Affiliation: Center of Applied Mathematics, School of Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
  • MR Author ID: 1027998
  • Email: zhoumingshuo@amss.ac.cn
  • Received by editor(s): January 10, 2021
  • Received by editor(s) in revised form: June 22, 2021
  • Published electronically: June 30, 2022
  • Additional Notes: The first author was supported by the NSFC (No. 11801391) and NSF of Jiangsu Province (No. BK20180832)
    The second and third authors were supported by the NSFC (No.11921001, No.11831013 and No.11501154).
    The third author was also supported by NSF of Zhejiang Province (No. LQ16A010005)
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 6015-6041
  • DOI: https://doi.org/10.1090/tran/8676
  • MathSciNet review: 4474883