6 papers
Some remarks on the Theorem
Yeongrak Kim, Hyunsuk Moon, Euisung Park
Let be a non-degenerate projective irreducible variety of dimension , degree , and codimension over an algebraically closed field of characte…
Geometric mean for T-positive definite tensors and associated Riemannian geometry
Jeong-Hoon Ju, Taehyeong Kim, Yeongrak Kim +1
In this paper, we generalize the geometric mean of two positive definite matrices to that of third-order tensors using the notion of T-product. Specifically, we define the geometri…
An Eisenbud-Goto type inequality for Stanley-Reisner ideals and simplicial complexes
Jaewoo Jung, Jinha Kim, Minki Kim +1
The Leray number of an abstract simplicial complex is the minimal integer where its induced subcomplexes have trivial homology groups in dimension or greater. We give an up…
Finding tensor decompositions with sparse optimization
Taehyeong Kim, Jeong-Hoon Ju, Yeongrak Kim
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank tensors. The main ingredient is the Least Absolute Shrinkage and…
A new formula of the determinant tensor with symmetries
Jeong-Hoon Ju, Taehyeong Kim, Yeongrak Kim
In this paper, we present a new formula of the determinant tensor for matrices. In \cite{kim2023newdet4}, Kim, Ju, and Kim found a new formula of …
Ulrich bundles on rational surfaces with an anticanonical pencil
Yeongrak Kim
Ulrich bundles are the simplest sheaves from the viewpoint of cohomology tables. Eisenbud and Schreyer conjectured that every projective variety carries an Ulrich bundle, which mea…