论文标题
通过曲曲面几何形状的镜头的理性紧张
Rational tensegrities through the lens of toric geometry
论文作者
论文摘要
经典的时态模型由矢量空间中的嵌入式图组成，其刚性条表示边缘，并将应力分配到每个边缘，以使应力在图形的每个顶点中总计为零。张力框架最近已从二维图案扩展到多维设置。我们使用曲折几何形状的工具研究了多维张力。对于给定的有理张力框架$ \ MATHCAL {f} $，我们构造了胶合式的感谢您的表面$ x_ \ Mathcal {f} $。我们表明，$ \ mathcal {f} $上的Abelian张力组是对Chow group $ a^1（x_ \ Mathcal {f}; \ qq）$的子组的同构。在平面框架的情况下，我们展示了如何通过曲折几何形状中的经典工具明确地进行张力计算。
A classical tensegrity model consists of an embedded graph in a vector space with rigid bars representing edges, and an assignment of a stress to every edge such that at every vertex of the graph the stresses sum up to zero. The tensegrity frameworks have been recently extended from the two dimensional graph case to the multidimensional setting. We study the multidimensional tensegrities using tools from toric geometry. For a given rational tensegrity framework $\mathcal{F}$, we construct a glued toric surface $X_\mathcal{F}$. We show that the abelian group of tensegrities on $\mathcal{F}$ is isomorphic to a subgroup of the Chow group $A^1(X_\mathcal{F};\QQ)$. In the case of planar frameworks, we show how to explicitly carry out the computation of tensegrities via classical tools in toric geometry.
