具有双曲轨道的复多项式向量场
Complex polynomial vector fields having a finitely curved orbit
摘要：
在本文中，我们解决了以下问题：（i）设$C\subset \mathbb C^2$是一个轨道的多项式向量场，具有有限的总高斯曲率。$C$是否包含在代数曲线中？(ii)对于一个具有超验轨道的多项式向量场，我们能说些什么呢？在一定的非退化条件下，我们对由向量场诱导的射影叶理的奇异性给出了肯定的回答。对于向量场与一个稍微更一般类的奇点，我们证明了一个分类结果，捕获合理的拉回庞加莱-杜拉克规范形式。
英文摘要：
In this paper we address the following questions: (i) Let $C\subset \mathbb C^2$ be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is $C$ contained in an algebraic curve? (ii) What can be said of a polynomial vector field which has a finitely curved transcendent orbit? We give a positive answer to (i) under some non-degeneracy conditions on the singularities of the projective foliation induced by the vector field. For vector fields with a slightly more general class of singularities we prove a classification result that captures rational pull-backs of Poincaré-Dulac normal forms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
