THE BIRATIONAL INVARIANTS OF LINS NETO'S FOLIATIONS

Hao Ling; Jun Lu; Sheng Li Tan

doi:10.1090/proc/16401

THE BIRATIONAL INVARIANTS OF LINS NETO'S FOLIATIONS

Hao Ling, Jun Lu, Sheng Li Tan

School of Mathematical Sciences

Nanjing Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5223-5238
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	12
DOIs	https://doi.org/10.1090/proc/16401
State	Published - 1 Dec 2023

Keywords

Chern number
Lins Neto's foliations
Zariski decomposition
slope inequality

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abstract = "Lins Neto [Ann. Sci. {\'E}cole Norm. Sup. (4) 35 (2002), pp. 231- 266] constructed families of foliations which are counterexamples to Poincar{\'e}'s Problem and Painlev{\'e}'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.",

keywords = "Chern number, Lins Neto's foliations, Zariski decomposition, slope inequality",

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N2 - 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.

AB - 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.

KW - Chern number

KW - Lins Neto's foliations

KW - Zariski decomposition

KW - slope inequality

UR - https://www.scopus.com/pages/publications/85175314737

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DO - 10.1090/proc/16401

M3 - 文章

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

THE BIRATIONAL INVARIANTS OF LINS NETO'S FOLIATIONS

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Keywords

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