On the slope of non-algebraic holomorphic foliations,Proceedings of the American Mathematical Society

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On the slope of non-algebraic holomorphic foliations
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-08-11 , DOI: 10.1090/proc/15097
Jie Hong , Jun Lu , Sheng-Li Tan

Abstract:Let $(Y, {\mathcal {G}})$ be a Riccati foliation on

and let $\pi :(X,{\mathcal {F}}){\rightarrow } (Y,{\mathcal {G}})$ be a double cover ramified over some normal-crossing curves. We will determine the minimal model of ${\mathcal {F}}$ and compute its Chern numbers $c_1^2({\mathcal {F}})$ , $c_2({\mathcal {F}})$ , and $\chi ({\mathcal {F}})=(c_1^2({\mathcal {F}})+ c_2({\mathcal {F}}))/12$ . We will prove that the slope $\lambda ({\mathcal {F}})=c_1^2({\mathcal {F}})/\chi ({\mathcal {F}})$ satisfies $4\leq \lambda ({\mathcal {F}})<12$ .

中文翻译：

非代数全同叶的斜率

摘要：让Riccati叶面在上面，让双重覆盖在一些法线交叉曲线上分叉。我们将确定的最小模型，并计算其数量陈省身，以及。我们将证明坡度满足要求。 $（Y，{\ mathcal {G}}）$

$\ pi：（X，{\ mathcal {F}}）{\ rightarrow}（Y，{\ mathcal {G}}）$ ${\数学{F}}$ $c_1 ^ 2（{\ mathcal {F}}）$ $c_2（{\ mathcal {F}}）$ $\ chi（{\ mathcal {F}}）=（c_1 ^ 2（{\ mathcal {F}}）+ c_2（{\ mathcal {F}}））/ 12$ $\ lambda（{\ mathcal {F}}）= c_1 ^ 2（{\ mathcal {F}}）/ \ chi（{\ mathcal {F}}）$ $4 \ leq \ lambda（{\ mathcal {F}}）<12$

更新日期：2020-09-02

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