论文标题
Bernstein-Kouchnirenko-Khovanskii与对称性
Bernstein-Kouchnirenko-Khovanskii with a symmetry
论文作者
论文摘要
具有规定的牛顿多层的通用多项式F（x，y，z）定义了对称空间曲线F（x，y，z）= f（y，y，x，z）= 0。我们研究其几何形状：其不可约组件的数量，程度和属，奇异性的数量和类型等，并讨论这些结果在多大程度上推广到更高的维度和更复杂的对称性。 作为一种应用，我们表征了复杂单变量多项式的通用单参数家族，其Galois组是一个完整的对称组。
A generic polynomial f(x,y,z) with a prescribed Newton polytope defines a symmetric spatial curve f(x,y,z)=f(y,x,z)=0. We study its geometry: the number, degree and genus of its irreducible components, the number and type of singularities, etc. and discuss to what extent these results generalize to higher dimension and more complicated symmetries. As an application, we characterize generic one-parameter families of complex univariate polynomials, whose Galois group is a complete symmetric group.
