关于马泰-萨利姆定理

arXiv - MATH - Complex Variables Pub Date : 2024-08-20 DOI:arxiv-2408.10767

Arturo Fernández-Pérez, Nancy Saravia-Molina

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摘要

我们扩展了马泰-萨利姆（Mattei-Salem）的一个定理，研究了复平面上的全形叶状$\mathcal{F}$的估值与$\mathcal{F}$的平衡分离方程的估值之间的关系。在某些条件下，我们还推导出了涉及复投影面上全形拓扑 $\mathcal{F}$ 的估值、切超量和度的不等式。

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On a Mattei-Salem theorem

We investigate the relationship between the valuations of a germ of a singular foliation $\mathcal{F}$ on the complex plane and those of a balanced equation of separatrices for $\mathcal{F}$, extending a theorem by Mattei-Salem. Under certain conditions, we also derive inequalities involving the valuation, tangency excess, and degree of a holomorphic foliation $\mathcal{F}$ on the complex projective plane.

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arXiv - MATH - Complex Variables

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