论文标题
在3个变量中的多项式多项式的无穷大分类
Classification at infinity of polynomials of degree 3 in 3 variables
论文作者
论文摘要
我们将3度的多项式的无限属性分类为3个变量，$ f（x_0，x_1，x_2）= f_1（x_0，x_1，x_1，x_1，x_2） + f_2（x_0，x_1，x_1，x_1，x_2） + f_3（x_0，x_1，x_1，x_2） 1,2,3 $。基于此分类，当我们从特殊纤维传递到通用纤维时，我们计算了无穷大的孤立奇异性的Milnor数量的跳跃。作为结果的应用，我们研究了$ \ mathbb {c}^3 $中3度多项式的全局纤维的存在，并搜索有关每个等价类中纤维拓扑的信息。
We classify singularities at infinity of polynomials of degree 3 in 3 variables, $ f (x_0, x_1, x_2) = f_1 (x_0, x_1, x_2) + f_2 (x_0, x_1, x_2) + f_3 (x_0, x_1, x_2) $, $ f_i $ homogeneous polynomial of degree $ i $, $ i = 1,2,3 $. Based on this classification, we calculate the jump in the Milnor number of an isolated singularity at infinity, when we pass from the special fiber to a generic fiber. As an application of the results, we investigate the existence of global fibrations of degree 3 polynomials in $\mathbb{C}^3$ and search for information about the topology of the fibers in each equivalence class.
