7 citations · 15 across the 11 of their papers we have counts for
12 papers
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 …
A new formula for the determinant of matrices
Taehyeong Kim, Jeong-Hoon Ju, Yeongrak Kim
In this paper, we present a new formula for the determinant of a matrix. We approach via the sparse optimization problem and derive the formula through the Least Absol…
Ulrich bundles on cubic fourfolds
Daniele Faenzi, Yeongrak Kim
We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 o…
Cubic forms having matrix factorizations by Hessian matrices
Yeongrak Kim
Using a part of XJC-correspondence by Pirio and Russo, we classify cubic forms whose Hessian matrices induce matrix factorizations of themselves. When it defines a reduced hype…
On the Borisov-Nuer conjecture and the image of the Enriques-to-K3 map
Marian Aprodu, Yeongrak Kim
We discuss the Borisov-Nuer conjecture in connection with the canonical maps from the moduli spaces of polarized Enriques surfaces with fixed polarization type…
An explicit matrix factorization of cubic hypersurfaces of small dimension
Yeongrak Kim, Frank-Olaf Schreyer
In this paper, we compute an explicit matrix factorization of a rank 9 Ulrich sheaf on a general cubic hypersurface of dimension at most 7, whose existence was proved by Manivel. I…
Ulrich bundles on intersections of two 4-dimensional quadrics
Yonghwa Cho, Yeongrak Kim, Kyoung-Seog Lee
In this paper, we investigate the existence of Ulrich bundles on a smooth complete intersection of two -dimensional quadrics in by two completely different methods…
Ulrich line bundles on Enriques surfaces with a polarization of degree four
Marian Aprodu, Yeongrak Kim
In this paper, we prove the existence of an Enriques surface with a polarization of degree four with an Ulrich bundle of rank one. As a consequence, we prove that general polarized…
Ulrich bundles on blowups
Yeongrak Kim
We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, w…
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…