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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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The birational invariants of Lins Neto’s foliations
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by Hao Ling, Jun Lu and Sheng-Li Tan
Proc. Amer. Math. Soc. 151 (2023), 5223-5238
DOI: https://doi.org/10.1090/proc/16401
Published electronically: September 20, 2023
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Abstract:

Lins Neto [Ann. Sci. École Norm. Sup. (4) 35 (2002), pp. 231–266] constructed families of foliations which are counterexamples to Poincaré’s Problem and Painlevé’s Problem. We will determine the minimal models of these families of foliations, calculate their Chern numbers, Kodaira dimension, and numerical Kodaira dimension. We prove that the slopes of Lins Neto’s foliations are at least 6, and their limits are bigger than $7$.
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Bibliographic Information
  • Hao Ling
  • Affiliation: School of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, People’s Republic of China
  • ORCID: 0000-0002-0586-4882
  • Email: hling@njit.edu.cn
  • Jun Lu
  • Affiliation: School of Mathematical Sciences, Shanghai Key Lab. of PMMP, East China Normal University, Shanghai 200241, People’s Republic of China
  • Email: jlu@math.ecnu.edu.cn
  • Sheng-Li Tan
  • Affiliation: School of Mathematical Sciences, Shanghai Key Lab. of PMMP, East China Normal University, Shanghai 200241, People’s Republic of China
  • ORCID: 0000-0001-6763-1681
  • Email: sltan@math.ecnu.edu.cn
  • Received by editor(s): July 19, 2022
  • Received by editor(s) in revised form: January 3, 2023
  • Published electronically: September 20, 2023
  • Additional Notes: This work was funded by the National Key Research and Development Program of China (Grant No. 2018AAA0101001), the National Natural Science Foundation of China (Grant No. 12331001), the Shanghai Science and Technology Commission Foundation (Grants No. 22DZ2229014 and No. 20511100200), the Scientific Research Foundation of Nanjing Institute of Technology (Grant No. YKJ201852), and the Horizontal Scientific Project of Nanjing Institute of Technology (Grant No. 3612415223089).
  • Communicated by: Jiaping Wang
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 5223-5238
  • MSC (2020): Primary 32S65, 14E20, 14D06, 37F75
  • DOI: https://doi.org/10.1090/proc/16401
  • MathSciNet review: 4648921