论文标题
平面上多项式图的热带判别
The tropical discriminant of a polynomial map on a plane
论文作者
论文摘要
多项式图的判别对于仿射几何学和奇异理论的问题至关重要。表征其表征的标准方法依赖于通常无效的消除技术。本文涉及在Puiseux系列领域定义的二维圆环上的多项式图。我们提出了一个组合程序，用于计算由具有给定支持的通用多项式确定的地图判别的热带曲线。我们的结果使一个人能够计算平面上复杂多项式图的判别式的牛顿多面。
The discriminant of a polynomial map is central to problems from affine geometry and singularity theory. Standard methods for characterizing it rely on elimination techniques that can often be ineffective. This paper concerns polynomial maps on the two-dimensional torus defined over a field of Puiseux series. We present a combinatorial procedure for computing the tropical curve of the discriminant of maps determined by generic polynomials with given supports. Our results enable one to compute the Newton polytope of the discriminant of complex polynomial maps on the plane.
