论文标题
结合多面体的实现空间模型
Combining realization space models of polytopes
论文作者
论文摘要
在本文中，我们研究了多个层的实现空间的四个不同模型：经典模型，格拉斯曼尼亚模型，大风变换模型和松弛品种。他们分别用矩阵来确定多面体的实现，其列是其顶点的坐标，所述矩阵的列空间，它们的大风变换和松弛矩阵。每个模型都用于研究多面体的实现。在本文中，我们非常明确地建立了使我们能够在模型之间移动，研究其确切关系并结合不同观点的优势的地图。作为例证，我们将格拉斯曼尼亚模型的紧凑性与松弛品种结合在一起，以获得减少的松弛模型，使我们能够执行以前无法计算范围的松弛理想计算。这些计算使我们能够回答[Criado，Santos。拓扑pr骨和小直径的小型较小球体。实验数学，1-13，2019]，讲述了一个pri骨家族的可靠性，通常通过证明其中一个人的不可证明性来证明否定性。
In this paper we examine four different models for the realization space of a polytope: the classical model, the Grassmannian model, the Gale transform model, and the slack variety. Respectively, they identify realizations of the polytopes with the matrix whose columns are the coordinates of their vertices, the column space of said matrix, their Gale transforms, and their slack matrices. Each model has been used to study realizations of polytopes. In this paper we establish very explicitly the maps that allow us to move between models, study their precise relationships, and combine the strengths of different viewpoints. As an illustration, we combine the compact nature of the Grassmannian model with the slack variety to obtain a reduced slack model that allows us to perform slack ideal calculations that were previously out of computational reach. These calculations allow us to answer the question of [Criado, Santos. Topological prismatoids and small simplicial spheres of large diameter. Experimental Mathematics, 1-13, 2019], about the realizability of a family of prismatoids, in general in the negative by proving the non-realizability of one of them.
