标题： 具有少量面的格拉斯曼流形中的正多面体 显示英文标题

标题： Positive Polytopes with Few Facets in the Grassmannian

摘要： 在本文中，我们研究通过将具有少量面的简单多面体在$\mathbb{P}^5$中与正交 Grassmannian$\mathrm{Gr}(2,4)$相交得到的几何对象的伴随超曲面。这些推广了正 Grassmannian，即$\mathrm{Gr}(2,4)$与单形的交集。我们证明，如果所得对象有五个面，则它是一个正几何，且伴随超曲面是唯一的。对于六个面的情况，我们证明伴随超曲面不一定是唯一的，并给出了伴随超曲面族维度的上限。我们通过一系列例子说明我们的结果。特别是，我们证明即使伴随超曲面不唯一，一个正六面体仍可以是正几何。 显示英文摘要

摘要： In this article we study adjoint hypersurfaces of geometric objects obtained by intersecting simple polytopes with few facets in $\mathbb{P}^5$ with the Grassmannian $\mathrm{Gr}(2,4)$. These generalize the positive Grassmannian, which is the intersection of $\mathrm{Gr}(2,4)$ with the simplex. We show that if the resulting object has five facets, it is a positive geometry and the adjoint hypersurface is unique. For the case of six facets we show that the adjoint hypersurface is not necessarily unique and give an upper bound on the dimension of the family of adjoints. We illustrate our results with a range of examples. In particular, we show that even if the adjoint is not unique, a positive hexahedron can still be a positive geometry.