Geometric Rank and Linear Determinantal Varieties

01/10/2022
by   Runshi Geng, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset