二元多项式无穷远处牛顿树的结构
Structure of the Newton tree at infinity of a polynomial in two variables
摘要：
设$f:\mathbb{C}^2 \to \mathbb{C}$是多项式映射。设$\mathbb{C}^2 \subset X$是$\mathbb{C}^2$的紧化，其中$X$是光滑有理紧曲面，使得存在扩张$f$的簇$Φ:X\to \mathbb{P}^1$的态射.放入$\mathcal{D}=X\setminus \mathbb{C}^2$ ; $\mathcal{D}$是一条不可约分支为光滑有理紧曲线且所有奇点为普通二重点的曲线。$\mathcal{D}$的对偶图是一棵树。我们感兴趣的是这棵树，我们分析其复杂性方面的属的通用纤维的$f$。
英文摘要：
Let $f:\mathbb{C}^2 \to \mathbb{C}$ be a polynomial map. Let $\mathbb{C}^2 \subset X$ be a compactification of $\mathbb{C}^2$ where $X$ is a smooth rational compact surface and such that there exists a morphism of varieties $Φ:X\to \mathbb{P}^1$ which extends $f$. Put $\mathcal{D}=X\setminus \mathbb{C}^2$; $\mathcal{D}$ is a curve whose irreducible components are smooth rational compact curves and all its singularities are ordinary double points. The dual graph of $\mathcal{D}$ is a tree. We are interested in this tree, and we analyse its complexity in terms of the genus of the generic fiber of $f$.
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。
