论文标题
几何等级和线性决定性品种
Geometric Rank and Linear Determinantal Varieties
论文作者
论文摘要
具有有界几何等级的三方张量与线性确定性品种之间有着密切的关系。我们研究了具有界定编码的线性决定性品种，并证明了环境空间的尺寸的上限。使用这些结果，我们将张量分类为几何等级3，找到具有几何级别4的原始张量的多线性等级的上限，并证明了这种上限一般存在。我们将三方张量的结果扩展到N部分张量，显示几何等级1和分区等级1之间的等效性。
There are close relations between tripartite tensors with bounded geometric ranks and linear determinantal varieties with bounded codimensions. We study linear determinantal varieties with bounded codimensions, and prove upper bounds of the dimensions of the ambient spaces. Using those results, we classify tensors with geometric rank 3, find upper bounds of multilinear ranks of primitive tensors with geometric rank 4, and prove the existence of such upper bounds in general. We extend results of tripartite tensors to n-part tensors, showing the equivalence between geometric rank 1 and partition rank 1.
