标题： 实变量二元多项式函数的分岔集和无穷远处奇点的牛顿多边形 显示英文标题

标题： The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity

摘要： 在本文中，我们通过使用一个环面紧化，确定了两个变量的实多项式函数在牛顿多边形意义下的非退化情况的分支集。 我们还在相同设定下计算了无穷远处的奇异现象的数量，称为“分裂”和“消失”。 最后，我们根据其牛顿多边形给出了分支集中元素数量的一个上界。 为了得到这个上界，我们依次对无穷远处的奇点应用环面变换。 显示英文摘要

摘要： In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at infinity, called "cleaving" and "vanishing" in the same setting. Finally, we give an upper bound of the number of elements in the bifurcation set in terms of its Newton polygon. To obtain the upper bound, we apply toric modifications to the singularities at infinity successively.