论文标题
未合力测量品种的线性对称性
Linear Symmetries of the Unsquared Measurement Variety
论文作者
论文摘要
我们介绍了一个新的代数品种系列，$ l_ {d，n} $，我们称之为未合资的测量品种。这个家庭被许多点$ n $和尺寸$ d $的参数化。这些品种自然来自刚性理论和距离几何形状的问题。在这些应用程序中，了解$ l_ {d，n} $的线性自动形态学组可能很有用。值得注意的是，Regge的结果意味着$ L_ {2,4} $具有意外的线性自动形态。在本文中，我们对所有$ n $和$ d $的$ l_ {d，n} $的线性自动形态的完整表征。我们表明，除了$ l_ {2,4} $之外，未合值的测量品种没有意外的自动形态。此外，对于$ l_ {2,4} $，我们表征完整的自动形态组。
We introduce a new family of algebraic varieties, $L_{d,n}$, which we call the unsquared measurement varieties. This family is parameterized by a number of points $n$ and a dimension $d$. These varieties arise naturally from problems in rigidity theory and distance geometry. In those applications, it can be useful to understand the group of linear automorphisms of $L_{d,n}$. Notably, a result of Regge implies that $L_{2,4}$ has an unexpected linear automorphism. In this paper, we give a complete characterization of the linear automorphisms of $L_{d,n}$ for all $n$ and $d$. We show, that apart from $L_{2,4}$ the unsquared measurement varieties have no unexpected automorphisms. Moreover, for $L_{2,4}$ we characterize the full automorphism group.
