论文标题
用于投影唯一性的代数方法，并应用了订购多塔的应用
An Algebraic Approach to Projective Uniqueness with an Application to Order Polytopes
论文作者
论文摘要
组合polytope $ p $据说，如果它具有单一的实现，则可以在投影转换方面进行唯一。投射唯一性是一种几何引人入胜的属性，但很难验证。在本文中，我们合并了两种文献中投影独特性的方法。一个主要是几何的，是由于麦克穆伦（McMullen）造成的，他表明某些自然操作可以保留投射唯一性。另一个更为代数，是由于Gouveia，Macchia，Thomas和Wiebe造成的。他们使用与多面关系相关的某些理想来验证一种称为图形性的属性，这意味着投射唯一性。在本文中，我们表明，麦克穆伦的操作不仅保留了投射的Uniquness，而且可以保留图形。作为应用程序，我们表明，大量的秩序多型家族是图形的，因此在投影上是独一无二的。
A combinatorial polytope $P$ is said to be projectively unique if it has a single realization up to projective transformations. Projective uniqueness is a geometrically compelling property but is difficult to verify. In this paper, we merge two approaches to projective uniqueness in the literature. One is primarily geometric and is due to McMullen, who showed that certain natural operations on polytopes preserve projective uniqueness. The other is more algebraic and is due to Gouveia, Macchia, Thomas, and Wiebe. They use certain ideals associated to a polytope to verify a property called graphicality that implies projective uniqueness. In this paper, we show that that McMullen's operations preserve not only projective uniquness but also graphicality. As an application, we show that large families of order polytopes are graphic and thus projectively unique.
