On the slope of non-algebraic holomorphic foliations

Jie Hong; Jun Lu; Sheng Li Tan

doi:10.1090/proc/15097

On the slope of non-algebraic holomorphic foliations

Jie Hong, Jun Lu, Sheng Li Tan

School of Mathematical Sciences

East China Normal University

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

3 Scopus citations

Abstract

Let (Y, G) be a Riccati foliation on Y and let π: (X, F)→(Y, G) be a double cover ramified over some normal-crossing curves. We will determine the minimal model of F and compute its Chern numbers c²₁(F), c2(F), and χ(F) = (c²₁(F) + c2(F))/12. We will prove that the slope λ(F) = c²₁(F)/χ(F) satisfies 4 ≤ λ(F) < 12.

Original language	English
Pages (from-to)	4817-4830
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	11
DOIs	https://doi.org/10.1090/proc/15097
State	Published - Nov 2020

Keywords

Chern number
Double cover
Riccati foliation
Slope inequality

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title = "On the slope of non-algebraic holomorphic foliations",

abstract = "Let (Y, G) be a Riccati foliation on Y and let π: (X, F)→(Y, G) be a double cover ramified over some normal-crossing curves. We will determine the minimal model of F and compute its Chern numbers c21(F), c2(F), and χ(F) = (c21(F) + c2(F))/12. We will prove that the slope λ(F) = c21(F)/χ(F) satisfies 4 ≤ λ(F) < 12.",

keywords = "Chern number, Double cover, Riccati foliation, Slope inequality",

author = "Jie Hong and Jun Lu and Tan, \{Sheng Li\}",

note = "Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",

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T1 - On the slope of non-algebraic holomorphic foliations

AU - Hong, Jie

AU - Lu, Jun

AU - Tan, Sheng Li

PY - 2020/11

Y1 - 2020/11

N2 - Let (Y, G) be a Riccati foliation on Y and let π: (X, F)→(Y, G) be a double cover ramified over some normal-crossing curves. We will determine the minimal model of F and compute its Chern numbers c21(F), c2(F), and χ(F) = (c21(F) + c2(F))/12. We will prove that the slope λ(F) = c21(F)/χ(F) satisfies 4 ≤ λ(F) < 12.

AB - Let (Y, G) be a Riccati foliation on Y and let π: (X, F)→(Y, G) be a double cover ramified over some normal-crossing curves. We will determine the minimal model of F and compute its Chern numbers c21(F), c2(F), and χ(F) = (c21(F) + c2(F))/12. We will prove that the slope λ(F) = c21(F)/χ(F) satisfies 4 ≤ λ(F) < 12.

KW - Chern number

KW - Double cover

KW - Riccati foliation

KW - Slope inequality

UR - https://www.scopus.com/pages/publications/85092755229

U2 - 10.1090/proc/15097

DO - 10.1090/proc/15097

M3 - 文章

AN - SCOPUS:85092755229

SN - 0002-9939

VL - 148

SP - 4817

EP - 4830

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

On the slope of non-algebraic holomorphic foliations

Abstract

Keywords

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