论文标题
当地的庞加莱问题
The local Poincaré problem for irreducible branches
论文作者
论文摘要
令$ {\ mathcal f} $为$ {\ Mathbb c}^{2} $的起源社区中定义的全态叶面的细菌，其具有不可恢复的全态不变性曲线$γ$。我们为$γ$的公式类别的$ {\ mathcal f} $的消失多样性提供了下限。此外，我们表明这样的下界很锋利。最后，我们表征了$ \ Mathcal {f} $的多重性可以根据$γ$的限制并在这种情况下提供明确绑定的界限。
Let ${\mathcal F}$ be a germ of holomorphic foliation defined in a neighborhood of the origin of ${\mathbb C}^{2}$ that has a germ of irreducible holomorphic invariant curve $γ$. We provide a lower bound for the vanishing multiplicity of ${\mathcal F}$ at the origin in terms of the equisingularity class of $γ$. Moreover, we show that such a lower bound is sharp. Finally, we characterize the types of dicritical singularities for which the multiplicity of $\mathcal{F}$ can be bounded in terms of that of $γ$ and provide an explicit bound in this case.
